JEE Main 2025 — Hyperbola Question with Solution
JEE Main 2025 (23 Jan Shift 1)
Question
Let the circle touch the line , have the centre on the positive x -axis, and cut off a chord of length along the line . Let H be the hyperbola , whose one of the foci is the centre of and the length of the transverse axis is the diameter of . Then is equal to ______
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Show full solutionCorrect answer: 19
Correct answer
19
Step-by-step explanation
Also $\begin{gathered} \Rightarrow\left(\frac{3 a-1}{\sqrt{13}}\right)^2+\frac{4}{13}=\frac{(a+1)^2}{2} \\ 5 a^2-14 a-3=0 \end{gathered}$ $\begin{aligned} & \because \quad a \neq-\frac{1}{5} \Rightarrow \\ & \Rightarrow \quad r=2 \sqrt{2} \end{aligned}$ One focus of is
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This is a previous-year question from JEE Main 2025, 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.