## Question

### Solution

Correct option is a = 4, the point (16, 16) corresponds to (at2, 2at) for t = 2.

ty = x + at2

is tangent and y = –tx + 2at + at3 is normal. Putting y = 0, we get

A(– at2, 0) = (–16, 0), B(2a + 2t2, 0) = (24, 0)

The circle through A, B, P will be on AB as diameter as . Hence center C is mid-point of AB is (4, 0).   #### SIMILAR QUESTIONS

Q1

If x + y = k is normal to y2 = 12x, then k is

Q2

A circle drawn on any focal chord AB of the parabola y2 = 4axas diameter cuts the parabola again at and D. If the parameters of the points A, B, C, D be t1, t2 t3 and t1 respectively, then the value of t3 t4 is

Q3

The length of normal chord which subtends an angle of 900 at the vertex of the parabola y2 = 4x is

Q4

A focal chord of parabola y2 = 4x is inclined at an angle of with the +ive direction of x-axis, then the slope of normal drawn at the ends of focal chord will satisfy the equation

Q5

If two different tangents of y2 = 4x are the normal’s to the parabola x2 = 4ay, then

Q6

Find the locus of the mid-points of the chord of the parabola y2 = 4ax which subtend a right angle at the vertex.

Q7

If the parabola C and D intersect at a point A on the line L1, then equation of the tangent point L at A to the parabola D is

Q8

If a > 0, the angle subtended by the chord AB at the vertex of the parabola is

Q9

P is a point on the circle C, the perpendicular PQ to the major axis of the ellipse E meets the ellipse at M, then is equal to