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Ellipse question

2025 · 28 Jan · Shift 1 · Q49

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JEE Main
Mathematics
Ellipse
2025 · 28 Jan · Shift 1 · Q49

Ellipse question

2025 · 28 Jan · Shift 1 · Q49

JEE MainMathematicsEllipseNumerical+4 / −1

Let

\mathrm{E}_1: \frac{x^2}{9}+\frac{y^2}{4}=1

be an ellipse. Ellipses

\mathrm{E}_{\mathrm{i}}

's are constructed such that their centres and eccentricities are same as that of

\mathrm{E}_1

, and the length of minor axis of

\mathrm{E}_{\mathrm{i}}

is the length of major axis of

E_{i+1}(i \geq 1)

. If

A_i

is the area of the ellipse

E_i

, then

\frac{5}{\pi}\left(\sum\limits_{i=1}^{\infty} A_i\right)

, is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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