The eccentricity of the ellipse with centre at the origin which meets the straight line `x/7 + y/2 = 1` on the axis of x and the straight line `x/3 - y/5 = 1` on the axis of y and whose axes lie along the axes of coordinates, is

Options

A. `(2sqrt6)/(7)`
B. `(3sqrt2)/(7)`
C. `(sqrt6)/(7)`
D. none of these

Answer

A

Explanation

Let the equation of the ellipse be `x^(2)/a^(2) + y^(2)/b^(2) = 1`.
It cuts the coordinate axes at (7,0) and (0, -5).
`therefore a = 7 and b = 5`
`therefore e = sqrt(1 - b^(2)/a^(2)) = sqrt(1 - 25/49) = (2sqrt6)/(7)`