TS EAMCET · Maths · Ellipse
\(S^{\prime}\) is the focus of the ellipse \(\frac{x^2}{25}+\frac{y^2}{b^2}=1,(b \lt 5)\) lying on the negative \(X\)-axis and \(P(\theta)\) is a point on this ellipse. If the distance between the foci of this ellipse is 8 and \(\mathbf{S P}=7\), then \(\theta=\)
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{2 \pi}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } 2 a c=8 \\ & S^{\prime} p=e\left(\frac{a}{e}+2\right) ; 7=a+e x=7 \\ & a e=4 ; e=\frac{4}{5} ; S^{\prime} P=7=5+\frac{4}{5} x \Rightarrow x=2.5 \\ & a \cos \theta=2.5 \Rightarrow \cos \theta=\frac{1}{2} \Rightarrow \theta=\frac{\pi}{3} .\end{aligned}
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