Mathematics

Problem

Let a line

L

pass through the point of intersection of the lines

bx + 10y - 8 = 0

and

2x - 3y = 0

b \in R - \left\{\frac{4}{3}\right\}

. If the line

L

also passes through the point

(1, 1)

and touches the circle

17(x^2 + y^2) = 16

, then the eccentricity of the ellipse

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

is : (a)

\frac{2}{\sqrt{5}}

(b)

\sqrt{\frac{3}{5}}

(c)

\frac{1}{\sqrt{5}}

(d)

\sqrt{\frac{2}{5}}