AP EAMCET · Maths · Hyperbola
If \(\sqrt{5} y-\sqrt{8}=0\) is the equation of the directrix of a hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}+1=0\) and \(\frac{\sqrt{5}}{2}\) is its eccentricity then \(\frac1a=\)
- A \(=\frac{1}{\sqrt{2}}\)
- B \(\sqrt{3}\)
- C \(\sqrt{5}\)
- D \(\sqrt{6}\)
Answer & Solution
Correct Answer
(A) \(=\frac{1}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
\(\frac{x^2}{a^2}-\frac{y^2}{b^2}+1=0\) i.e. \(\frac{y^2}{b^2}-\frac{x^2}{a^2}=1\) It is conjugate hyperbola Equation of directrix must be \(y=\frac{b}{e}\) Comparing with \(\sqrt{5} y-\sqrt{8}=0\)…
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