JEE Main 2020MathematicsHyperbolaMediumMCQ

JEE Main 2020 — Hyperbola Question with Solution

JEE Main 2020 (08 Jan Shift 2)

Question

If a hyperbola passes through the point P10, 16, and it has vertices at ±6, 0, then the equation of the normal to it at P, is.

Choose an option

Show full solutionCorrect option: B
Correct answer
B2x+5y=100

Step-by-step explanation

Let the equation of hyperbola is x2a2-y2b2=1.

As, vertex is at ±6,0, and it passes through 10, 16,
So, the equation of hyperbola is x236-y2144=1.
Equation of normal to the hyperbola at x1, y1 is a2xx1+b2yy1=a2+b2

Thus, on putting values, equation of normal is 2x+5y=100.

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About this question

This is a previous-year question from JEE Main 2020, 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.