Question

(3,4), (5,12) are two foci of the ellipse passing through the origin. Then the eccentricity of the ellipse is

• A. $\frac{\sqrt{17}}{3}$
• B. $\frac{2\sqrt{17}}{3}$
• C. $\frac{\sqrt{34}}{3}$
• D. $\frac{\sqrt{17}}{9}$

Answer 1

Answer: (D)

$\frac{\sqrt{17}}{9}$

Answer 2

Since P= (0, 0) is a point on the ellipse

SP +S’P = 2a where S = (3, 4) and S’ (5, 12)

∴ 5 + 13 = 2a ⇒ a =9

but SS’ = 2ae

2$\sqrt{17}$ = 2 x 9 x e

⇒ e = $\sqrt{17}$/9.