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, ~b R-\4/3. If the line L also passes through the point (1,1) and touches the circle 17(x²+y²)=16, then the eccentricity of the ellipse (x²)/5+(y²)/(~b²)=1 is:

Coordinate Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 29 Jul, Morning shift · Q3764

JEE Main 202229 Jul, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

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 :