QJEEM22Ma4c0f: JEE Main 2022 Mathematics - Class 11 JEEM22Ma4c0f Solution: If the ellipse x 2 a 2 + y 2 b 2 = 1 meets the line x 7 + y 2 6 …

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QJEEM22Ma4c0f: JEE Main 2022 Mathematics - Class 11 JEEM22Ma4c0f Solution: If the ellipse x 2 a 2 + y 2 b 2 = 1 meets the line x 7 + y 2 6 …

If the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ meets the line $\frac{x}{7} + \frac{y}{2 \sqrt{6}} = 1$ on the $x$ -axis and the line $\frac{x}{7} - \frac{y}{2 \sqrt{6}} = 1$ on the $y$ -axis, then the eccentricity of the ellipse is :

Multiple Choice Options

A 57
B 267
C 37
D 257

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Accepted Answer

$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ meets the line $\frac{x}{7} + \frac{y}{2 \sqrt{6}} = 1$ on the x-axis

So, $a = 7$

and $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ meets the line $\frac{x}{7} - \frac{y}{2 \sqrt{6}} = 1$ on the y-axis

So, $b = 2 \sqrt{6}$

Therefore, $e^{2} = 1 - \frac{b^{2}}{a^{2}} = 1 - \frac{24}{49}$

$e = \frac{5}{7}$

QJEEM22Ma4c0f: JEE Main 2022 Mathematics - Class 11 JEEM22Ma4c0f Solution: If the ellipse x 2 a 2 + y 2 b 2 = 1 meets the line x 7 + y 2 6 …

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