JEE Main 2022MathematicsParabolaMediumMCQ

JEE Main 2022 — Parabola Question with Solution

JEE Main 2022 (29 Jun Shift 2)

Question

Let P:y2=4ax, a>0 be a parabola with focus S.Let the tangents to the parabola P make an angle of π4 with the line y=3x+5 touch the parabola P at A and B. Then the value of a for which A, B and S are collinear is:

Choose an option

Show full solutionCorrect option: D
Correct answer
Dany a>0

Step-by-step explanation

Lines making angle π4 with y=3x+5 

So using formula tanα=m2-m11+m1m2, we have slope -2 & 12.

Which are perpendicular to each-other so, A, S, Bare collinear for all a>0. (by property that perpendicular tangents will lie on directrix and chord of contact will pass through focus, so the points are collinear )

   

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About this question

This is a previous-year question from JEE Main 2022, covering the Parabola chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.