JEE Main 2022MathematicsParabolaMediumMCQ

JEE Main 2022 — Parabola Question with Solution

JEE Main 2022 (25 Jul Shift 2)

Question

The tangents at the points A1,3 and B1,-1 on the parabola y2-2x-2y=1 meet at the point P. Then the area (in unit2) of the triangle PAB is:

Choose an option

Show full solutionCorrect option: D
Correct answer
D8

Step-by-step explanation

Given,  y2-2x-2y=1 

⇒y-12=2x+1

Tangents are drawn at 1,3 & 1,-1, on plotting the diagram we get,

​​​​​​​

Now, tangent as A: 2y-x-5=0 {using T=0}

Intersection with y=1 is x=-3

Hence, point P is -3,1

We can see diagram has symmetry

So, area of ∆PAB=2×12×1--3×3-1

=8 sq.units

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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.