TS EAMCET · Maths · Hyperbola
\(P(\theta)\) is a point on the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{9}=1, \mathrm{~S}\) is its focus lying on the positive X -axis and \(\mathrm{Q}=(0,1)\). If \(S Q=\sqrt{26}\) and \(\mathrm{SP}=6\), then \(\theta=\)
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{3}\)
- D \(\cos ^{-1}\left(\frac{2}{3}\right)\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } S Q^2=26=a^2 e^2+1 \\ & \Rightarrow a e=5 \Rightarrow e^2=\frac{25}{a^2}=1+\frac{b^2}{a^2}=1+\frac{9}{a^2} \\ & \Rightarrow \frac{25}{a^2}-\frac{9}{a^2}=1 \Rightarrow a=4, e=\frac{5}{4} \\ & P=(4 \sec \theta, 3 \tan \theta) \\ & P S^2=(4 \sec…
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