JEE Main 2021MathematicsHyperbolaMediumMCQ

JEE Main 2021 — Hyperbola Question with Solution

JEE Main 2021 (26 Aug Shift 2)

Question

The locus of the mid points of the chords of the hyperbola x2-y2=4, which touch the parabola y2=8x, is :

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Show full solutionCorrect option: A
Correct answer
Ay2x-2=x3

Step-by-step explanation

Equation of chord of hyperbola x2-y2=4 with mid-point h, k is given by xh-yk=h2-k2

⇒yk=xh-h2+k2

⇒y=hxk+k2-h2k

This will touch the parabola y2=8x, if

⇒k2-h2k=2h/k

⇒2kh=k2-h2k

⇒h3+2k2-k2 h=0
∴ Equation of locus is x3+2y2-y2x=0 

⇒ x3=y2x-2

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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.