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Ellipse question

2022 · 29 Jul · Shift 1 · Q32

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PYQ Library
JEE Main
Mathematics
Ellipse
2022 · 29 Jul · Shift 1 · Q32

Ellipse question

2022 · 29 Jul · Shift 1 · Q32

JEE MainMathematicsEllipseMCQ+4 / −1

Let a line L pass through the point of intersection of the lines

b x+10 y-8=0

and

2 x-3 y=0, \mathrm{~b} \in \mathbf{R}-\left\{\frac{4}{3}\right\}

. If the line

\mathrm{L}

also passes through the point

(1,1)

and touches the circle

17\left(x^{2}+y^{2}\right)=16

, then the eccentricity of the ellipse

\frac{x^{2}}{5}+\frac{y^{2}}{\mathrm{~b}^{2}}=1

is :

A
$\frac{2}{\sqrt{5}}$
B
$\sqrt{\frac{3}{5}}$
C
$\frac{1}{\sqrt{5}}$
D
$\sqrt{\frac{2}{5}}$

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