COMEDK · Maths · 14. Ellipse
If the area of the auxillary circle of the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b)\) is twice the area of the ellipse, then the eccentricity of the ellipse is
- A \(\frac{\sqrt{3}}{2}\)
- B \(\frac{1}{\sqrt{2}}\)
- C \(\frac{1}{2}\)
- D \(\frac{1}{\sqrt{3}}\)
Answer & Solution
Correct Answer
(A) \(\frac{\sqrt{3}}{2}\)
Step-by-step Solution
Detailed explanation
Equation of ellipse is \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) Then, equation of auxillary circle will be \[ x^{2}+y^{2}=a^{2} \quad(a>b) \] Now, it is given that Area of auxillary circle \(=2 \times\) Area of ellipse…
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