Question

If the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets the line $\frac{x}{7}+\frac{y}{2 \sqrt{6}}=1$ on the $x$-axis and the line $\frac{x}{7}-\frac{y}{2 \sqrt{6}}=1$ on the $y$-axis, then the eccentricity of the ellipse is

• A. $\frac{5}{7}$
• B. $\frac{2 \sqrt{6}}{7}$
• C. $\frac{3}{7}$
• D. $\frac{2 \sqrt{5}}{7}$

Answer 1

Answer: (A)

$\frac{5}{7}$

Answer 2

Ellipse a2x2​+b2y2​=1 passes through the point (7,0) and (0,−26​)
Now a249​+0=1⇒a2=49
and 0+b224​=1⇒b2=24
Now a>b⇒b2=a2(1−e2)
⇒24=49(1−e2)⇒e2=4925​⇒e=75​