Assignment Details

Conic Sections

1448 minutes

Apr 19, 7:52 PM

300.0 marks

MCQ

135 questions

black blood

Class Details

Engineering maths

11th

Engineering maths

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Question Text

Question 1 :
The product of the lengths of perpendiculars drawn from any point on the hyperbola x2 - 2y2 - 2 = 0 to its asymptotes, is-

Question 2 :
Find the equation of the circle through the point (-2, 4) and through the points of intersection of the circle x2 + y2 - 2x - 6y + 6 = 0 and the line 3x + 2y - 5 = 0

Question 3 :
Equation of the circle, whose diameter is the chord x + y = 1 of the circles x2 + y2 = 4, is -

Question 4 :
The line y = x - 6 is a normal to the parabola y2=8x. Then the foot of the normal is

Question 5 :
If the line {tex} x = m y + k {/tex} touches the parabola {tex} x ^ { 2 } = 4 a y , {/tex} then what is the value of {tex} k ? {/tex}

Question 6 :
The straight lines joining the origin to the points of intersection of the line <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7be5a6f3020298ca1352a"> with the curve <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7be5ac2a2ae2953d94079">

Question 7 :
A man running round a race course notes that the sum of the distances of two flag-posts from him is always 10 metres and the distance between the flag-posts is 8 metres. The area of the path he encloses in square metres is-

Question 8 :
If y+b = m1(x+a) and y+b = m2(x+a) are two tangents to the parabola y2 = 4ax, then

Question 9 :
The product of the lengths of perpendiculars drawn from any point on the hyperbola x2 - 2y2 - 2 = 0 to its asymptotes, is-

Question 10 :
If x+y+k = 0 is a tangent to the parabola x2 = 4y, then k =

Question 11 :
If the points (2,-1), (5,k) are conjugate w.r.t. x2 = 8y, then k =

Question 12 :
If xy = m2 - 9 be a rectangular hyperbola whose branches lie only in the second and fourth quadrant, then -

Question 13 :
If the coordinate at one end of diameter of the circle: x2 + y2 - 8x - 4y + c = 0 are (-3,2), the coordinate at the other end are

Question 14 :
The equation of a line passing through the centre of a rectangular hyperbola is x - y - 1 = 0. If one of its asymptotes is 3x - 4y - 6 = 0, the equation of the other asymptote is

Question 15 :
A circle {tex} S {/tex} of radius {tex} ^ { \prime } a ^ { \prime } {/tex} is the director circle of another circle {tex} S _ { 1 } {/tex} . {tex} S _ { 1 } {/tex} is the director circle of circle {tex} S _ { 2 } {/tex} and so on. If the sum of the radii of all these circles is {tex} 2 , {/tex} then the value of {tex} a {/tex} is

Question 16 :
The equation of the parabola whose vertex is {tex} ( - 1 , - 2 ) , {/tex} axis is vertical, and which passes through the point {tex} ( 3,6 ) , {/tex} is

Question 17 :
Tangents are drawn from the point P(-1, 6) to the circle x2 + y2 - 4x - 6y + 4 = 0. If A and B are the points of contact of these tangents and 'O' be the centre of the circle, then area of quadrilateral PAOB is-

Question 18 :
If the line x + 2by + 7 = 0 is a diameter of the circle x2 + y2 - 6x + 2y = 0, then b =

Question 19 :
Let AB be a chord of the circle x2 + y2 = r2 subtending a right angle at the centre, then the locus of the centroid of the triangle PAB as P moves on the circle is

Question 20 :
An ellipse is described by using an endless string which is passed over two pins. If the axes are 6 cm and 4 cm, the necessary length of the string and the distance between the pins respectively in cm, are

Question 21 :
The diameter of a parabolic reflector is 12cm and its depth is 4cm. The position where the bulb on the axis is to be placed at a distance from vertex is equal to

Question 22 :
The common tangent to the parabolas y2 = 4ax and x2 = 32 ay has the equation-

Question 23 :
Area of the triangle formed by the lines x - y = 0, x + y = 0 and any tangent to the hyperbola x2 - y2 = a2 is-

Question 24 :
The equation of the tangents drawn at the ends of the major axis of the ellipse 9x2 + 5y2 - 30y = 0, are-

Question 25 :
The slopes of two tangents drawn from (1, 4) to the parabola y2 = 12x are

Question 26 :
The ends of latus rectum of parabola {tex} x ^ { 2 } + 8 y = 0 {/tex} are

Question 27 :
The line y = 2t2 meets the ellipse <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e7499c8f511820358e67c13' height='43' width='79' > in real points if

Question 28 :
The area of the triangle inscribed in the parabola y2 = 4x, whose vertices are given by t1= ½ , t2 = 1, t3 = 2 is

Question 29 :
The radical centre of three circles described on the three sides of a triangle as diameter is the

Question 30 :
If P1Q1 and P2Q2 are two focal chords of parabola y2 = 4ax then the chords P1 P2 and Q1Q2 intersect on the-

Question 31 :
The equation of the ellipse whose one of the vertices is (0, 7) and the corresponding directrix is y = 12, is

Question 32 :
Find the length of the tangent drawn from the point {tex} ( 5,1 ) {/tex} to the circle {tex} x ^ { 2 } + y ^ { 2 } + 6 x - 4 y - 3 = 0 {/tex}

Question 33 :
The equation of the parabola whose vertex is at (2, -1) and focus at (2, -3) is

Question 34 :
If hyperbola x2 - y2 = a2 and xy = c2 are of same size, then:

Question 35 :
The locus of a point which moves such that the difference of its distances from two fixed points is always a constant, is

Question 36 :
The centre of a set of circles, each of radius 3, lie on x2 + y2 = 25 . The locus of any point in the set is

Question 37 :
The line y = mx + c will be a normal to the circle with radius r and centre at (a, b), if -

Question 38 :
If the latusrectum of the ellipse x2tan2α + y2sec2α = 1 is ½, then α =

Question 39 :
The length of the latus rectum of the parabola {tex} x ^ { 2 } - 4 x - 8 y {/tex} {tex} + 12 = 0 {/tex} is

Question 40 :
The vertex of a parabola is the point {tex} ( a , b ) {/tex} and latus rectum is of length {tex} l . {/tex} If the axis of the parabola is along the positive direction of {tex} y {/tex} -axis, then its equation is

Question 41 :
The equation of the tangent to the parabola {tex} y = x ^ { 2 } - x {/tex} at the point where {tex} x = 1 , {/tex} is

Question 42 :
The length of the common chord of the ellipse <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e749bbc46f7eb01d9e6d784' height='43' width='140' > and the circle (x - 1)2 + (y - 2)2 = 1:

Question 43 :
A tangent to y2 = 16x is y = 4x + 1. Point on this tangent from which a perpendicular tangent can be drawn to same parabola :

Question 44 :
If two distinct chords drawn from the point (4, 4) on the parabola y2 = 4ax are bisected on the line y = mx, then the set of value of m is given by-

Question 45 :
The coordinates of the middle point of the chord {tex} 2 x - 5 y + 18 = 0 {/tex} cut off by the circle {tex} x ^ { 2 } + y ^ { 2 } - 6 x + 2 y - 54 = 0 {/tex} is

Question 46 :
If tangents PQ and PR are drawn from point P to <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e749caf46f7eb01d9e6d886' height='40' width='23' >-<img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e749caff511820358e67f52' height='40' width='23' >= 1 (a > b); so that fourth vertex S of parallelogram PQSR lie on circumcircle of triangle PQR, then locus of P is-

Question 47 :
Equation of hyperbola passing through origin and whose asymptotes are 3x + 4y = 5 and 4x + 3y = 5, is-

Question 48 :
If PCP' and DCD' be a pair of conjugate diameter of an ellipse <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e7499c6f511820358e67c11' height='47' width='79' > whose centre is C then (CP)2 + (CD)2 equals.

Question 49 :
The area of portion of the circle x2 + y2 - 4y = 0 lying below x-axis is -

Question 50 :
If the focus of a parabola is (2, -1) and directrix has the equation x+y = 3, then the vertex is

Question 51 :
A wheel of radius 8 units rolls along the diameter of a semicircle of radius 25 units it bumps into this semicircle. What is the length of the portion of the diameter that cannot be touched by the wheel ?

Question 52 :
The abscissae and ordinate of the end points A and B of a focal chord of the parabola y2 = 4x are respectively the roots of equations x2 - 3x + a = 0 and y2 + 6y + b = 0. The equation of the circle with AB as diameter, is -

Question 53 :
Let {tex} O {/tex} be the vertex and {tex} Q {/tex} be any point on the parabola, {tex} x ^ { 2 } = {/tex} {tex} 8y {/tex} . If the point {tex} P {/tex} divides the line segment {tex} O Q {/tex} internally in the ratio {tex} 1 : 3 , {/tex} then the locus of {tex} P {/tex} is

Question 54 :
Let {tex} P Q {/tex} be a double ordinate of the parabola, {tex} y ^ { 2 } = - 4 x {/tex} , where {tex} P {/tex} lies in the second quadrant. If {tex} R {/tex} divides {tex} P Q {/tex} in the ratio {tex} 2 : 1 {/tex} then the locus of {tex} R {/tex} is

Question 55 :
The slope of the line touching both the parabolas {tex} y ^ { 2 } = 4 x {/tex} and {tex} x ^ { 2 } = - 32 y {/tex} is

Question 56 :
A chord is drawn through the focus of the parabola {tex} y ^ { 2 } = 6 x {/tex} such that its distance from the vertex of this parabola is {tex} \frac { \sqrt { 5 } } { 2 } {/tex} , then its slope can be

Question 57 :
If the line x - 1 = 0 is the directrix of the parabola y2 - kx + 8 = 0, k ≠ 0 and the parabola intersects the circle x2 + y2 = 4 in two real distinct points, then the value of k is-

Question 58 :
The normal to a curve at P(x, y) meets the x-axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a

Question 59 :
AB is a diameter of x2 + 9y2 = 25. The eccentric angle of A is π/6. Then the eccentric angle of B is -

Question 60 :
The abcissa and ordinate of the end points A and B of a focal chord of the parabola y2 = 4x are respectively the roots of x2 - 3x + a = 0 and y2 + 6y + b = 0. The equation of the circle with AB as diameter is.

Question 61 :
Tangents are drawn from a point P to the parabola y2 = 8x such that the slope of one tangent is twice the slope of other. The locus of P is

Question 62 :
The combined equation of the asymptotes of the hyperbola 2x2 + 5xy + 2y2 + 4x + 5y = 0.

Question 63 :
The line 3x + 2y + 1 = 0 meets the hyperbola 4x2 - y2 = 4a2 in the points P and Q. The coordinates of the point of intersection of the tangents at P and Q are

Question 64 :
AB is a chord of the parabola y2 = 4ax with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the x-axis is-

Question 65 :
The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex is x-y+1=0 is

Question 66 :
Let y2 = 4ax be parabola and PQ be a focal chord of parabola. Let T be the point of intersection of tangents at P and Q. Then

Question 67 :
The name of the conic represented by the equation x2 + y2 - 2xy + 20x + 10 = 0 is-

Question 68 :
If the chord of contact of tangents from a point P to the parabola y2 = 4ax, touches the parabola x2 = 4by, then the locus of P is a/an -

Question 69 :
Tangents PA and PB are drawn to x2 = 4ay, if m1& m2 be the slopes of these tangents and m12 + m22 = 4 then locus of P is

Question 70 :
For the hyperbola x2sec2α-y2cosec2α = 1 which of the following remains constant with the changes of α.

Question 71 :
If the tangent to the ellipse x2 + 4y2 = 16 at the point P(θ) is a normal to the circle x2 + y2 - 8x - 4y = 0, then θ equals

Question 72 :
If the tangent at the point (4 cos φ , (16/√11) sin φ) to the ellipse 16x2 + 11y2 = 256 is also a tangent to the circle x2 + y2 - 2x = 15, then the value of φ is-

Question 73 :
The equation of the common tangent touching the circle (x - 3)2 + y2 = 9 and the parabola y2 = 4x above the x-axis is -

Question 74 :
Consider a focal chord PQ of the parabola y2 = 4ax, a∈ R+. Tangent drawn at P and normal drawn at Q meet the axis of the parabola at T and N respectively. Let P be (at2, 2at). If angle between PT and QN is 'α' and distance between PT and QN is 'd', then

Question 75 :
The centre of the circle passing through the point (0, 1) and touching the curve y = x2 at (2, 4) is

Question 76 :
The point on the curve y2 = 4x which is nearest to (2, 1) is

Question 77 :
The common tangents to the circle x2 + y2 = a2/2 and the parabola y2 = 4ax intersect at the focus of the parabola-

Question 78 :
The normal to the rectangular hyperbola xy = c2 at the point 't' meets the curve again at a point 't' such that

Question 79 :
A line L passing through the focus of the parabola y2 = 4 (x - 1) intersects the parabola in two distinct points. If 'm' be the slope of the line L then-

Question 80 :
If cos α = 2/3, then range of the values of φ for which the point φ on the ellipse x2 + 4y2 = 4 falls inside the circle x2 + y2 + 4x + 3 = 0 is:

Question 81 :
If a circle makes intercepts of length 5 and 3 on two perpendicular lines, then the locus of the centre of the circle is

Question 82 :
The area of the parallelogram formed by the tangents at the ends of conjugate diameters of an ellipse is -

Question 83 :
If the line ax +by + c = 0 is a tangent to the parabola y2 - 4y - 8x + 32 = 0, then -

Question 84 :
If P1Q1 & P2Q2 or are two focal chords of y2 = 4ax then the chord P1P2& Q1Q2 intersect on

Question 85 :
Set of values of 'h' for which the number of distinct common normals of (x - 2)2 = 4(y - 3) and x2 + y2 - 2x - hy - c = 0 (c > 0) is 3, is

Question 86 :
If the tangents and normals at the extremities of a focal chord of a parabola intersect at (x1, y1) and (x2, y2) respectively, then-

Question 87 :
The number of points with integral coordinates that lie in the interior of the region common to the circle x2 + y2 = 16 and the parabola y2 = 4x is -

Question 88 :
If the line lx + my + n = 0 meets the hyperbola <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e749ab346f7eb01d9e6d655' height='41' width='52' > = 1 at the extremities of a pair of conjugate diameters, then the relation a2 - b2m2 is equal to -

Question 89 :
The tangent at the point A(12, 6) to a parabola intersects its directrix at the point B(-1, 2). The focus of the parabola lies on x-axis. The number of such parabolas is-

Question 90 :
If the tangent at the point P(x1,y1) to the parabola y2 = 4ax meets the parabola y2 = 4a(x + b) at Q and R, then the mid-point of QR is-

Question 91 :
If equation (10x - 5)2 + (10y - 4)2 = λ2 (3x + 4y - 1)2 represents a hyperbola, then -

Question 92 :
PA and PB are the tangents drawn to y2 = 4x from point P. These tangents meet the y-axis at the points A1 and B1 respectively. If the area of triangle PA1 B1 is 2 sq. units, then locus of 'p' is-

Question 93 :
A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P, Q, R and S. Then CP2 + CQ2 + CR2 + CS2 is equal to

Question 94 :
Tangent to the curve y = x2 + 6 at a point P(1, 7) touches the circle x2 + y2 + 16x + 12y + c = 0 at a point Q. Then the coordinate of Q are-

Question 95 :
Number of points from where perpendicular tangents to the curve <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7bd51ab3481716f4b6b75"> can be drawn, is

Question 96 :
The length of the chord cut off by y = 2 x + 1 from the circle x2 + y2 = 2, is

Question 97 :
Two perpendicular tangents PA and PB are drawn to curve y2 = kx, where k is maximum value of (2<img style='object-fit:contain' align="bottom" height="23" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5fc0e531e6377b2e815f29ea" width="21"/> sin  + 2cos ) and if p is the length of AB satisfying in equation log2log3log4 p < 0, then the range of p is-

Question 98 :
The point of the straight line y = 2x + 11 which is nearest to the circle 16(x2+y2) + 32x − 8y − 50 = 0, is

Question 99 :
A, B, C and D are the points of intersection with the coordinate axes of the lines ax + by = ab and bx + ay = ab, then

Question 100 :
The length of the latus rectum of the hyperbola xy - 3x - 3y + 7 = 0 is:

Question 101 :
The slope of the normal at the point (at2, 2 at) of the parabola, y2 = 4ax, is

Question 102 :
The Cartesian equation of the directrix of the parabola whose parametric equations are x = 2t + 1, y = t2 + 2, is

Question 103 :
The locus of the mid point of the chord of the circle x2 + y2 − 2x − 2y − 2 = 0 which makes an angle of 120∘ at the centre, is

Question 104 :
The line $3x + 5y = 15\sqrt{2}$ is a tangent to the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1,$ at a point whose eccentric angle is

Question 105 :
On the ellipse 4x2 + 9y2 = 1 the point at which the tangent are parallel to 8x = 9y are

Question 106 :
Any point on the hyperbola $\frac{\left( x + 1 \right)^{2}}{16} - \frac{\left( y - 2 \right)^{2}}{4} = 1$ is of the form

Question 107 :
For the hyperbola $\frac{x^{2}}{\cos^{2}\alpha} - \frac{y^{2}}{\sin^{2}\alpha} = 1$, which of the following remains constant when α varies?

Question 108 :
The line x + 2y + 3 = 0 and its conjugate with respect to the parabola y2 = 4x are perpendicular to each other. The equation of the conjugate line is

Question 109 :
If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 − 3ax + dy − 1 = 0 intersect in two distinct points P and 𝒬, then the line 5x + by − a = 0 passes through P and 𝒬 for

Question 110 :
If the line 3x − 4y − k = 0, (k > 0) touches the circle x2 + y2 − 4x − 8y − 5 = 0 at (a, b), then k + a + b is equal to

Question 111 :
The area of the circle whose centre is at (2, 3) and passing through (4, 6), is

Question 112 :
The equation of the tangent to the parabola y2 = 8x which is perpendicular to the line x − 3y + 8 = 0 is

Question 113 :
If tangents at A and B on the parabola y2 = 4ax intersect at point C, then ordinates of A, C and B are

Question 114 :
A tangent to the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ cuts the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ in P and Q. The locus of the mid-point of PQ is

Question 115 :
The circles x2 + y2 + x + y = 0 and x2 + y2 + x − y intersect at an angle of

Question 116 :
Let {tex} C {/tex} be a curve given by {tex} y ( x ) = 1 + \sqrt { 4 x - 3 } , x > \frac { 3 } { 4 } . {/tex} If {tex} P {/tex} is a point on {tex} C , {/tex} such that the tangent at {tex} P {/tex} has slope {tex} \frac { 2 } { 3 } {/tex} then a point through which the normal at {tex} P {/tex} passes, is

Question 117 :
The line y = mx + 1 is a tangent to the parabola y2 = 4x, if

Question 118 :
AB, AC are tangents to a parabola y2 = 4ax; p1, p2, p3 are the lengths of the perpendiculars from A, B, C on any tangent to the curve, then p2, p1, p3 are in

Question 119 :
If P(at12, 2at1) and Q(at22, 2at2) are two variable points on the curve y2 = 4 ax and PQ subtends a right angle at the vertex, then t1t2 is equal to

Question 120 :
Two perpendicular tangents to y2 = 4ax always intersect on the line, if

Question 121 :
Circle x2 + y2 − 2x − λx − 1 = 0 passes through two fixed points coordinates of the points are

Question 122 :
Coordinates of foci of hyperbola are (-5,3) and (7, 3) and eccentricity is 3/2. Then ,length of its latusrectum is

Question 123 :
If the circles x2 + y2 + 4x + 8y = 0 and x2 + y2 + 8x + 2ky = 0 touch each other, then k is equal to

Question 124 :
If P is a point such that the ratio of the squares of the lengths of the tangents from P to the circles x2 + y2 + 2x − 4y − 20 = 0 and x2 + y2 − 4x + 2y − 44 = 0 is 2 : 3, then the locus of P is a circle with centre

Question 125 :
If the normal at the end of latusrectum of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ passes through (0, − b), then e4 + e2(where e is eccentricity) equals

Question 126 :
The equation of the tangent at the vertex of the parabola x2+4x+2y = 0 is

Question 127 :
The length of the latusrectum of the ellipse $\frac{x^{2}}{36} + \frac{y^{2}}{49} = 1$ is

Question 128 :
Equation of the circle passing through the intersection of ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ and $\frac{x^{2}}{b^{2}} + \frac{y^{2}}{a^{2}} = 1$, is

Question 129 :
Tangents PT1 and PT2 are drawn from a point P to the circle x2 + y2 = a2. If the point P lies on the line px + qy − r = 0, then the locus of the circumcircle of the triangle P T1T2

Question 130 :
The length of the latus-rectum of the parabola ay2 + by = x - c is-

Question 131 :
A straight rod of length 9 units with its ends A, B always on x and y axes respectively. then, the locus of the centroid of Δ OAB, is

Question 132 :
The length of latusrectum of the ellipse 9x2 + 16y2 = 144 is

Question 133 :
The curve represented by the equation 4x2 + 16y2 − 24x − 32y − 12 = 0 is

Question 134 :
Let AB be a chord of the circle x2 + y2=r2 subtending a right angle at the4 centre. Then, the locus of the centroid of the Δ PAB as P moves on the circle is

Question 135 :
Three normals to the parabola y2 = x through point (a, 0). Then,

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