TS EAMCET · Maths · Hyperbola
If the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1,(a>b)\) has eccentricity and the length of the latusrectum respectively equal to \(\frac{5}{4}\) and 9 , then \(a b\) is equal to
- A \(12 \sqrt{2}\)
- B \(18 \sqrt{3}\)
- C 48
- D 20
Answer & Solution
Correct Answer
(C) 48
Step-by-step Solution
Detailed explanation
Eccentricity \((e)=\sqrt{1+\frac{b^2}{a^2}}\) \[ \begin{aligned} \Rightarrow & 1+\frac{b^2}{a^2} =\frac{25}{16} \quad given \\ \Rightarrow & b^2 =\frac{9}{16} a^2 \end{aligned} \] and length of latus rectum \(=9\)(given)…
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