TS EAMCET · Maths · Ellipse
The product of the lengths of the perpendiculars drawn from the two foci of the ellipse \(\frac{x^2}{9}+\frac{y^2}{25}=1\) to the tangent at any point on the ellipse is
- A \(6\)
- B \(7\)
- C \(8\)
- D \(9\)
Answer & Solution
Correct Answer
(D) \(9\)
Step-by-step Solution
Detailed explanation
(1) Product of length of perpendicular from focii to a tangent of ellipse \(=(\text { semi minor axis })^2\) \(\therefore \quad\) For \(\frac{x^2}{9}+\frac{y^2}{25}=1\) Semi minor axis \(=3\) \(\therefore \quad\) Product of lengths of perpendiculars \(=9\).
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