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FOUNDATION QUESTIONS EXERCISE, , 1 Equation of the parabola whose vertex is (—1,-2),, axis is, vertical and which passes through the point (3, 6) is, (a) x? + 4x + 28y-136=0, (b) 2 + 2x-2y-3=0, (c) y+ 4y-16x- 12=0, (d) None of the above, 2 A focal chord of the parabola y’ = 8x in inclined to X-axis, at an angle tan 3. Then its length is equal to, (a) 80/3 (b) 80/9 (c) 40/3 (d) 40/9, 3 Latus rectum of the parabola whose axis is parallel to the, Y-axis and which passes through the points (0, 4), (1, 9),, and (-2, 6) is equal to, (a) 1/2 (b) 1 (c)2, 4 If the line x -1= is the directrix of the parabola, y’ kx + 8=0, then one of the value of k is, ais (b) 8 (c)4 (d) 1/4, 5 The locus of trisection point of any double ordinate of the, parabola y? = 4axis, (a) y° =9ax (b) y? =ax, (c) 9y? = 4ax (d) None of these, , (d) None of these, , , , , , 6 Let Obe the vertex and Q be any point on the parabola, x? = By. If the point P divides the line segment OQ, internally in the ratio1:3, then the locus of Pis, ~~ JEE Mains 2015, (a) x’ =y (b) y’, ()y? =2x (d) x’, 7 Atany points P on the parabola y® - 2y - 4x +5=0,a, tangent is drawn which meets the directrix at Q the locus of, , , , the points R which divides QP externally in the ratio} Lis, , (a) (+1) (1-y+4=0 (b) x+1=0, (c) (- yy -4=0 (a) None of these, 8 The line x—b+ Ay =0 cuts the parabola y = 4ax at, Plat,’ ,2at,) and Q(at3, 2at,). If b ¢[2a, 4a] and 4 R, then, t,t, belongs to, (a) --4,-2], (c) [-3,-2], 9 The centre of the circle passing through the point (0, 1) and, touching the curve y = x? at (2, 4)is, , © (5) (549), , () (=e 3) (d) None of these, 5 10,, , (b) [4,-3], (d) None of these, , 10 Equation of common tangents to parabolas y = x? and, y=-x? +4x —4is/are, (a) y=4(x-Diy=0, (c) y=O y=-10(x + 5), , (b)y=0,y=-4 (x=, (d) None of these, , , , , , 11 Angle between the tangents drawn from the point (1, 4), to the parabola y? = 4x is, (a) x6 (b) n/a, (c) x/3 (d) 2, , 12 Ifthe lines y~b=m, (x +a)and y—b=m, (x +a)are, , , , 13 Set of values of h for which the number of distinct, common normals of (x —2)* = 4(y—3) and, x? +y® —2x—hy—c = Owhere, (c > 0)is 3, is, (a) Q=) (b) (4,29) (c) 24) (d) 10.), 14 Tangent and normal are drawn at P(16,16) on the, parabola y” =16x, which intersect the axis of the, parabola at A and B respectively. If Cis the centre of, the circle through the points P, A and 8 and ZCPB =,, then a value of tan@ is * JEE Mains 2018, , @t (2 (0)3 ws, , 15 Pis a point on the parabola y* = 4x and Qis a point, on the line 2x + y + 4=0. Ifthe line xy +1=0 is, the perpendicular bisector of PQ, then the coordinates, of Pis, , (a) (8, 9), (10, 11) () (1,-2),@-6, , (c) (7,8), (9,8) (d) None of these, , 16 The locus of the vertices of the family of parabolas, abx?, = a* —2ais, , 3° 2, , (a) xy = 105/64, , (c) xy = 35/16, , 17 The parabola y? = Ax, and 25 [(x-3) +(y+2)']=(8x-4y-2), are equal, if & is equal to, , (a) 1 (b) 2 (c) 3 (d) 6, , 18 Aline is drawn from A(-2,0)to intersect the curve, , y? = 4x in Pand@Q in the first quadrant such the, , — 1 <1 then'slope of the line is always, , , , , , (b) xy = 3/4, (d) xy = 64/105,, , 303, , , , AP" AQ” 4, (a) < v3 (b) > V3, (c) 2v3 (d) None of these, , 19 Vertex A of a parabola y’ = 4ax is joined to any point P, on it and line PQ is drawn at right angle to AP to meet, the axis at Q. Then, the projection of PQ on the axis is, always equal to, , (a) 3a (b) 2a, (c) V3a (d) 4a