Question

If (5, 12) and (24, 7) are the foci of a conic passing through the origin then the eccentricity of conic is-

• A. $\frac{\sqrt{386}}{12}$
• B. $\frac{\sqrt{386}}{38}$
• C. $\frac{\sqrt{386}}{25}$
• D. $\sqrt{2}$

Answer 1

Answer: (A)

$\frac{\sqrt{386}}{12}$

Answer 2

If two foci be S(5, 12) and S¢(24, 7) and it passes through origin O.

Then SO = $\sqrt{25 + 144}$ = 13 ; S¢O = $\sqrt{576 + 49}$ = 25 and SS¢ = $\sqrt{386}$

If conic be an ellipse, then SO + S¢O = 2a and SS¢ = 2ae

\ e = $\frac{SS'}{SO + S'O}$ = $\frac{\sqrt{386}}{38}$

IF conic be a hyperbola, then

S¢O – SO = 2a and SS¢ = 2ae

\ e = $\frac{SS'}{S'O–SO}$ = $\frac{\sqrt{386}}{12}$.