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TS EAMCET · Maths · Ellipse

Tangents are drawn to the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\) at all the four ends of its latusrectum. Then, the area (in sq units) of the quadrilateral formed by these tangents is

  1. A \(\frac{125}{6}\)
  2. B \(\frac{250}{3}\)
  3. C \(\frac{80}{3}\)
  4. D \(\frac{260}{3}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{250}{3}\)

Step-by-step Solution

Detailed explanation

Given that, equation of ellipse \( \frac{x^2}{25}+\frac{y^2}{16}=1 \Rightarrow \frac{x^2}{5^2}+\frac{y^2}{4^2}=1 \) So, \( a=5, b=4 \) Eccentricity, \(e=\sqrt{1-\left(\frac{16}{25}\right)}\) \(\left[\because e=\sqrt{1-\frac{b^2}{a^2}}\right]\) \( =\sqrt{\frac{25-16}{25}} \)…