TS EAMCET · Maths · Ellipse
If \(F_1\) and \(F_2\) are the focii of the ellipse \(16 x^2+25 y^2=400\) and \(P\) is any point on it, then the value of the product \(P F_1 \cdot P F_2\) lie in the interval
- A [16,25]
- B [0,16]
- C [25,400]
- D [0,400]
Answer & Solution
Correct Answer
(A) [16,25]
Step-by-step Solution
Detailed explanation
Given, equation of ellipse \(16 x^2+25 y^2=400\) \(\Rightarrow \frac{x^2}{25}+\frac{y^2}{16}=1\), Comparing to \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) Then, \(a=5\) and \(b=4\) Let \(P(5 \cos \theta, 4 \sin \theta)\) be any point on the ellipse. Then,…
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