JEE Main 2019MathematicsHyperbolaMediumMCQ

JEE Main 2019 — Hyperbola Question with Solution

JEE Main 2019 (10 Apr Shift 1)

Question

If a directrix of a hyperbola centered at the origin and passing through the point 4,-23 is 5x=45 and its eccentricity is e, then:

Choose an option

Show full solutionCorrect option: B
Correct answer
B4e4-24e2+35=0

Step-by-step explanation

Let equation of hyperbola is x2a2-y2b2=1

∴ It passes through 4, -23  ⇒16a2-12b2=1

⇒16-12×a2b2=a2...1

Equation of directrix is x=ae=45, given in question.

⇒a2=165e2...2

And we know that b2=a2e2-1

⇒b2a2=e2-1...3

∴ From 1,2 & 3

16-12e2-1=165e2

⇒16e2-16-12=16e25e2-1

⇒ 4e4-24e2+35=0   

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About this question

This is a previous-year question from JEE Main 2019, 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.