AP EAMCET · Maths · Hyperbola
If a directrix of a hyperbola centred at the origin and passing through the point \((4,-2 \sqrt{3})\) is \(\sqrt{5} x=4\) and \(e\) is its eccentricity, then \(e^2=\)
- A \(\frac{\sqrt{7}}{2}\)
- B \(\frac{7}{2}\)
- C \(\frac{35}{4}\)
- D \(2 \sqrt{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{7}{2}\)
Step-by-step Solution
Detailed explanation
Since hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) passes through \((4,-2 \sqrt{3})\) \(\therefore \frac{16}{a^2}-\frac{12}{b^2}=1 \Rightarrow 16-12 \frac{a^2}{b^2}=a^2\) \(\qquad ...\mathrm{(i)}\) Directrix : \(\sqrt{5} x=4 \Rightarrow \frac{4}{\sqrt{5}}=\frac{a}{e}\)…
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