PrepRung
Sign inSign up free

JEE Main 2022 · Mathematics · Conic Sections · medium

On the parabola y^2=12x, a first-quadrant point P is 7 units away from the focus. The y-coordinate of P is

Single correct option

On the parabola y2=12xy^2=12x, a first-quadrant point PP is 77 units away from the focus. The yy-coordinate of PP is
  1. A. 66
  2. B. 232\sqrt3
  3. C. 434\sqrt3
  4. D. 88
Show answer and solution

Answer: (C) 434\sqrt3

For y2=12xy^2=12x, 4a=124a=12 so a=3a=3 and the focus is (3,0)(3,0). The focal distance of a point is x+a=x+3=7x+a=x+3=7, giving x=4x=4. Then y2=12⋅4=48y^2=12\cdot4=48 and y=43y=4\sqrt3 in the first quadrant. The value 6 comes from wrongly using the latus rectum endpoints.
Report a mistake

Original question written in the JEE Main 2022 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake