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AP EAMCET · Maths · Ellipse

If \(\mathrm{A}_1, \mathrm{~A}_2, \mathrm{~A}_3\) are the areas of ellipse \(x^2+4 y^2-4=0\) its director circle and auxiliary circle respectively, then \(\mathrm{A}_2+\mathrm{A}_3-\mathrm{A}_1=\)

  1. A \(11 \pi\)
  2. B \(3 \pi\)
  3. C \(7 \pi\)
  4. D \(9 \pi\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(7 \pi\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text { } x^2+4 y^2-4=0 \\ & \Rightarrow \frac{x^2}{4}+\frac{y^2}{1}=1, \Rightarrow a^2=4, b^2=1 \end{aligned}\) Equation of director circle is \(x^2+y^2=a^2+b^2 \Rightarrow x^2+y^2=5\) Equation of Auxiliary circle is \(x^2+y^2=a^2 \Rightarrow x^2+y^2=4\)…