Question

A conic passing through origin has its foci at $\left(5,12\right)\&\left(24,7\right)$. then its eccentricity of hyperbola is

• A. $\frac{\sqrt{386}}{12}$
• B. $\frac{\sqrt{386}}{39}$
• C. $\frac{\sqrt{386}}{47}$
• D. $\frac{\sqrt{386}}{51}$

Answer 1

The correct option is A $\frac{\sqrt{386}}{12}$

Given that,

Foci at (5,12) and (24,7)

Then we know that,

Distance between foci in hyperbola $=2ae=\sqrt{{(24-5)}^2+{(7-12)}^2}=\sqrt{{19}^2+{(-5)}^2}=\sqrt{386}$ …….. (1)

Also,

Foci radii=$2a=\sqrt{{24}^2+7^2}-\sqrt{5^2+{12}^2}$

$=25-13=12$ …….. (2)

Divide equation (1) and (2) to,

$\frac{2ae}{2a}=\frac{\sqrt{386}}{12}$

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