TS EAMCET · Maths · Hyperbola
If the latus rectum through one of the foci of a hyperbola \(\frac{x^2}{9}-\frac{y^2}{b^2}=1\) subtends a right angle at the farther vertex of the hyperbola, then \(b^2=\)
- A \(4\)
- B \(16\)
- C \(25\)
- D \(27\)
Answer & Solution
Correct Answer
(D) \(27\)
Step-by-step Solution
Detailed explanation
\(a^2=9\) \(\left(\frac{\frac{b^2}{a}}{ae-(-a)}\right) \left(\frac{-\frac{b^2}{a}}{ae-(-a)}\right) = -1\) \(\frac{-b^4}{a^4(e+1)^2} = -1 \Rightarrow b^2 = a^2(e+1)\) \(a^2(e^2-1) = a^2(e+1)\) \(e^2-1 = e+1 \Rightarrow e^2-e-2=0 \Rightarrow (e-2)(e+1)=0\)…
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