JEE Advanced | 2017CircleHard

Question

If a chord, which is not a tangent, of the parabola  y2 = 16x has the equation 2x + y = p, and midpoint (h, k), then which of the following is(are) possible value(s) of p, h and k ?

Options

A.

p = 5, h = 4, k = -3

B.

p = -1, h = 1, k = -3

C.

p = -2, h = 2, k = -4

D.

p = 2, h = 3, k = -4

Solution

y2 = 16x,

2x + y = p … (i)

Equation of chord having mid point (h, k) is T = S1

yk – 8(x + h) = k2 – 16h

 yk – 8x = k2 - 8h … (ii)

Comparing (i) and (ii)

k1=-81=k2-8hp

⇒k= - 4 and k2  - 8h = – 4p

⇒16 – 8h = -4p

 ⇒2h - p = 4

Clearly h = 3, p = 2

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