JEE Main 2021MathematicsHyperbolaHardMCQ

JEE Main 2021 — Hyperbola Question with Solution

JEE Main 2021 (18 Mar Shift 2)

Question

Consider a hyperbola H : x2-2y2=4. Let the tangent at a point P(4,6) meet the x-axis at Q and latus rectum at Rx1,y1,x1>0. If F is a focus of H which is nearer to the point P, then the area of ΔQFR (in sq. units) is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C76-2

Step-by-step explanation

x24-y22=1

e=1+b2a2=32

∴ Focus F(ae,0)⇒F(6,0)

equation of tangent at P to the hyperbola is
2x-y6=2

tangent meet x-axis at Q(1,0)

& latus rectum x=6 at R6,266-1

∴ Area of ΔQFR=126-1·266-1

=76-2 sq. units

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Hyperbola chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2021, covering the Hyperbola 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.