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JEE Advanced 2017Paper 1
Exam
JEE Advanced
Year
2017
Paper
Paper 1
Subject
Mathematics
Chapter
Parabola

JEE Advanced 2017 · Paper 1 · Mathematics · Parabola

If a chord, which is not a tangent, of the parabola y ^ 2 = 16x has...

If a chord, which is not a tangent, of the parabola y2=16x{y}^{2} = 16x has the equation 2x+y=p2x + y = p, and midpoint (h, k), then which of the following is (are) possible value(s)ofp,hof p, h and kk?

Options

  1. Ap=−2,h=2,k=−4p = - 2, h = 2, k = - 4
  2. Bp=5,h=4,k=−3p = 5, h = 4, k = - 3
  3. Cp=−1,h=1,k=−3p = - 1, h = 1, k = - 3
  4. Dp=2,h=3,k=−4p = 2, h = 3, k = - 4

Correct answer

D. p=2,h=3,k=−4p = 2, h = 3, k = - 4

Step-by-step solution

Equation of chord with mid point (h,k)( h, k ):

k.y−16(x+h2)=k2−16hk . y - 16\left(\dfrac{x + h}{2}\right) = {k}^{2} - 16h

⇒8x−ky+k2−8h=0⇒ 8x - ky + {k}^{2} - 8h = 0

Comparing with 2x+y−p=0,2x + y - p = 0, we get

k=−4;2h−p=4k = - 4; 2h - p = 4

Only p=2,h=3,k=−4p = 2, h = 3, k = - 4 satisfies above relation.

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