TS EAMCET · Maths · Ellipse
If \(S\) and \(S^{\prime}\) are the foci of the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\) and if \(P S P^{\prime}\) is a focal chord with \(S P=8\), then \(S S^{\prime}\) is equal to
- A \(4+S^{\prime} P\)
- B \(S^{\prime} P-1\)
- C \(4+S P\)
- D \(S P-1\)
Answer & Solution
Correct Answer
(A) \(4+S^{\prime} P\)
Step-by-step Solution
Detailed explanation
Given equation of ellipse \( \frac{x^2}{25}+\frac{y^2}{16}=1 \) Here, \(a=5\) and \(b=4\) \( \begin{aligned} e & =\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{16}{25}} \\ & =\sqrt{\frac{9}{25}}=\frac{3}{5} \end{aligned} \) Also, \(\quad P S+P S^{\prime}=2 {a}=2 \times 5=10\)…
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