JEE Main 2021 — Hyperbola Question with Solution
From: JEE Main 2021 (Online) 27th August Evening Shift
Question
Let A (sec, 2tan) and B (sec, 2tan), where + = /2, be two points on the hyperbola 2x2 y2 = 2. If (, ) is the point of the intersection of the normals to the hyperbola at A and B, then (2)2 is equal to ____________.
Enter your answer
Show full solutionCorrect answer: 2
Correct answer
2
Step-by-step explanation
Since, point A (sec, 2tan) lies on the hyperbola 2x2 y2 = 2
Therefore, 2sec2 4tan2 = 2
2 + 2tan2 4tan2 = 2
tan = 0 = 0
Similarly, for point B, we will get = 0.
but according to question + = which is not possible.
Hence, it must be a 'BONUS'.
Therefore, 2sec2 4tan2 = 2
2 + 2tan2 4tan2 = 2
tan = 0 = 0
Similarly, for point B, we will get = 0.
but according to question + = which is not possible.
Hence, it must be a 'BONUS'.
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.