Question

The eccentricity of the ellipse 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 co-ordinate, is-

• A. $\frac{3\sqrt{2}}{7}$
• B. $\frac{2\sqrt{3}}{7}$
• C. $\frac{\sqrt{3}}{7}$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

We have x/7 + y/2 = 1

\ the straight line cut the x-axis, at A(7, 0) and the straight line x/3 – y/5 = 1 cut the y-axis at B (0, –5).

Let the equation of the ellipse be x²/a² + y²/b² = 1it is given that it passes through A & B. Therefore, a² = 49 & b² = 25

\ The eccentricity of the ellipse is e

= $\sqrt{\left( 1 - \frac{b^{2}}{a^{2}} \right)} = \sqrt{1 - \frac{25}{49}} = \frac{2\sqrt{6}}{7}$.