AP EAMCET · Maths · Ellipse
Let \(E_1=\frac{x^2}{9}+\frac{y^2}{4}=1\) and \(E_2=\frac{x^2}{d^2}+\frac{y^2}{b^2}=1\) be two ellipses and \(\mathrm{R}\) be a rectangle with sides parallel to the coordinate axes. Let \(E_1\) be inscribed ellipse in \(\mathrm{R}\) and \(E_2\) be circumscribed ellipse on R. If \(E_2\) passes through \((0,4)\) then
- A \(a=4, b=2 \sqrt{3}\)
- B \(a=12, b=16\)
- C \(a=16, b=16\)
- D \(a=2 \sqrt{3}, b=4\)
Answer & Solution
Correct Answer
(D) \(a=2 \sqrt{3}, b=4\)
Step-by-step Solution
Detailed explanation
Acc. to question. \(\begin{aligned} & E_1=\frac{x^2}{g}+\frac{y^2}{4}=1 \Rightarrow a=3, b=2 \\ & E_2=\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\end{aligned}\) \(\because \mathrm{E}_2\), passes through \((0,4)\) \(\Rightarrow b= \pm 4\) for \(E_2\) from figure \(C=(3,2)\)…
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