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TS EAMCET · Maths · Ellipse

If P is any point on the ellipse \(\frac{x^2}{25}+\frac{y^2}{9}=1\) and \(\mathrm{S}, \mathrm{S}^{\prime}\) are its foci, then the maximum area (in sq. units) of \(\Delta \mathrm{SPS}^{\prime}=\)

  1. A \(15\)
  2. B \(12\)
  3. C \(6\)
  4. D \(25\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(12\)

Step-by-step Solution

Detailed explanation

\(a^2=25, b^2=9 \implies a=5, b=3\) \(c^2=a^2-b^2=25-9=16 \implies c=4\) \(A_{\Delta SPS'} = \frac{1}{2} \times (2c) \times |y| = c|y|\) \(A_{max} = c \times b = 4 \times 3 = 12\)