JEE Main 2017 — Hyperbola Question with Solution
From: JEE Main 2017 (Offline)
Question
A hyperbola passes through the point P and has foci at . Then the tangent to this hyperbola at P also passes through the point :
Choose an option
Show full solutionCorrect option: A
Correct answer
A
Step-by-step explanation
Equation of hyperbola is
foci is (±2, 0)
ae = 2
a2e2 = 4
Since b2 = a2 (e2 – 1)
b2 = a2 e2 – a2
a2 + b2 = 4 .....(1)
Also Hyperbola passes through
(b2 – 3) (b2 + 4) = 0
b2 = 3 or b2 = -4
For b2 = 3
a2 = 1
Equation of tangent is
It satisfy point .
foci is (±2, 0)
ae = 2
a2e2 = 4
Since b2 = a2 (e2 – 1)
b2 = a2 e2 – a2
a2 + b2 = 4 .....(1)
Also Hyperbola passes through
(b2 – 3) (b2 + 4) = 0
b2 = 3 or b2 = -4
For b2 = 3
a2 = 1
Equation of tangent is
It satisfy point .
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This is a previous-year question from JEE Main 2017, 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.