Question 1 :
The distance between $M(-1,5)$ and $N(x,5)$ is $8$ units. The value of $x$ is:
Question 2 :
The points $(-2, -1), (1, 0),(4, 3),$ and $(1, 2)$ are the vertices
Question 3 :
The distance between the points $(a , b)$ and $(-1, -b)$ is 
Question 5 :
The slope of the line passing through the points $A(-2, 1)$ and $B(0, 3)$ is:<br/>
Question 7 :
The value of $k$ when the distance between the points $(3, k)$ and $(4, 1)$ is $\sqrt{10}$ is <br/>
Question 8 :
The slope of the line joining $(1, 2) $ and $(1, 3)$ is ____
Question 9 :
If the points $(1,0), (0,1)$ and $(x,8)$ are collinear, then the value of $x$ is equal to<br>
Question 10 :
If a point (x, y) in a OXY-plane is equidistant from $(-1, 1)$ and $(4, 3)$, then.<br>
Question 11 :
$A$ is the point on the y-axis whose ordinate is $5$ and $B$ is the point $(-3, 1)$. Calculate the length of $AB$.
Question 12 :
If the points $A(3, 4)$, $B(7, 12)$ and $P(x, x)$ are such that $(PA)^{2}> (PB)^{2}> (AB)^{2},$ then integral value of $x$ can be
Question 13 :
The vertices of a triangle are $A(3,4)$, $B(7,2)$ and $C(-2, -5)$. Find the length of the median through the vertex A.<br/>
Question 14 :
$ABC$ is an equilateral triangle. If the coordinates of two of its vertices are ($1, 3)$ and $(-2, 7)$ the coordinates of the third vertex can be<br>
Question 15 :
The points given are $(1, 1)$, $(-2, 7)$ and $(3, 3)$.Find distance between the points.
Question 16 :
State whether the following statements are true or false.<br/>The equation $x^{2}+y^{2} + 2x -10y + 30 = 0$ represents the equation of a circle.<br/>
Question 17 :
The equation to the circle with centre $(2,1)$ and touches the line $3x+4y-5$ is ?<br/>
Question 18 :
Find the equation of the circle passing through the origin and centre lies on the point of intersection of the lines $2x+y=3$ and $3x+2y=5$.
Question 20 :
The least value of $2x^{2} + y^{2} + 2xy + 2x - 3y + 8$ for real numbers $x$ and $y$ is
Question 21 :
Which of the following equations of a circle has center at (1, -3) and radius of 5?
Question 22 :
The centre of the circle given by $\mathbf { r } \cdot ( \mathbf { i } + 2 \mathbf { j } + 2 \mathbf { k } ) = 15 \text { and } | \mathbf { r } - ( \mathbf { j } + 2 \mathbf { k } ) | = 4 ,$
Question 23 :
Find the equation of the circle : <br>Centered at $(3,-2)$ with radius $4$.
Question 24 :
Assertion: If the equation of a circle is $(x+1)^2+(y-1)^2=4$, then its radius is 4.
Reason: Equation of a circle with radius r is given by, $(x-a)^2 + (y-b)^2=r^2$.
Question 26 :
What is the radius of the circle with the following equation?<br>$\displaystyle x^{2}-6x+y^{2}-4y-12=0$<br>
Question 28 :
The length of the diameter of the circle ${x^2} + {y^2} - 4x - 6y + 4 = 0$
Question 29 :
The parabola $y = px^{2} + px + q$ is symmetrical about the line
Question 33 :
A circle has a diameter whose ends are at (-3, 2) and (12, -6) Its Equation is
Question 34 :
If the equation $ax^{2}+2(a^{2}+ab-16)xy+by^{2}2ax+2by-\sqrt[4]{2}=0$ represents a circle, the radius of the circle is
Question 35 :
Find the value of a if $y^2=4ax $ pases through $(8,8)$
Question 36 :
If the vertex $= (2, 0)$ and the extremities of the latus rectum are $(3, 2)$ and $(3, -2)$, then the equation of the parabola is 
Question 37 :
The length of the latus rectum of the parabola $169 \left[(x-1)^2+(y-3)^2\right]=(5x-12y+17)^2$ is:
Question 38 :
On the parabola $y={ x }^{ 2 }$, the point least distant from the straight line $y=2x-4$ is
Question 39 :
The equation of the tangent to the curve y = 2sinx + sin2x at $x=\frac { \pi }{ 3 } $ on it is
Question 40 :
If the circle $x^{2}+y^{2}=9$ passesthrough $(2,c)$ then $c$ is equal to 
Question 41 :
Assertion: The length of latus rectum of the parabola whose parametric equation is $\displaystyle x = t^{2} + t + 1$ & $\displaystyle y = t^{2} - t + 1$ for $\displaystyle t \: \in \: R$ is equal to $\displaystyle 2$.
Reason: The length of the latus rectum of the parabola $\displaystyle y^{2} = 4ax$ is $\displaystyle 4a$.
Question 42 :
The lines $2x-3y=5$ and $3x-4y=7$ are the diameters of a circle of area $154$ sq.units. The equation of the circle is
Question 43 :
If a be the radius of a circle which touches<i> x-axis</i> at the origin, then its equation is <br><br>
Question 44 :
Equation of the circle which passes through the centre of the circle ${x}^{2}+{y}^{2}+8x+10y-7=0$ and is concentric with the circle $2{x}^{2}+2{y}^{2}+8x-12y-9=0$ is
Question 45 :
A circle is concentric with circle $x^{2}+ y^{2}-2x+4y-20=0$. If perimeter of the semicircle is $36$ then the equation of the circle is :
Question 46 :
The graph of the curve $x^2 + y^2 - 2xy - 8x - 8y + 32 = 0$ falls wholly in the
Question 47 :
Find the equation of the circle with center at $(-3,5)$ and passes through the point $(5,-1)$
Question 48 :
The circle passing through $\left(t,1\right),\left(1,t\right)$ and $\left(t,t\right)$ for all values of $t$ also passes through
Question 49 :
If the line $3x+4y=24$ and $4x+3y=24$ intersects the coordinates axes at $A,B,C$ and $D$, then the equation of the circle passing through these $4$ points  is<br/>
Question 50 :
The curve described parametrically by$x = {t^2} + t + 1$ and $y = {t^2} - t + 1$ represents
