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Ellipse question

2023 · 6 Apr · Shift 2 · Q33

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JEE Main
Mathematics
Ellipse
2023 · 6 Apr · Shift 2 · Q33

Ellipse question

2023 · 6 Apr · Shift 2 · Q33

JEE MainMathematicsEllipseMCQ+4 / −1

In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of persons, who speak only English is

\alpha

and the number of persons who speak only Hindi is

\beta

, then the eccentricity of the ellipse

25\left(\beta^{2} x^{2}+\alpha^{2} y^{2}\right)=\alpha^{2} \beta^{2}

is :

A
$\frac{\sqrt{129}}{12}$
B
$\frac{3 \sqrt{15}}{12}$
C
$\frac{\sqrt{119}}{12}$
D
$\frac{\sqrt{117}}{12}$

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