COMEDK · Maths · 15. Hyperbola
If the latusrectum of a hyperbola subtends a right angle at the other focus, then its eccentricity is
- A \(\sqrt{3}+1\)
- B \(\sqrt{2}+1\)
- C \(\sqrt{3}+\sqrt{2}\)
- D 2
Answer & Solution
Correct Answer
(B) \(\sqrt{2}+1\)
Step-by-step Solution
Detailed explanation
\(\tan \frac{\pi}{4}=\frac{L S}{S_{1} S}\) \(\begin{aligned} &=\frac{a\left(e^{2}-1\right)}{2 a e} \\ \Rightarrow \quad 1 &=\frac{e^{2}-1}{2 e} \\ \Rightarrow e^{2}-2 e-1 &=0 \end{aligned}\) Solving, \(\quad e=\sqrt{2}+1\)
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