Question

The radius of the director circle of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is:

• A. $a-b$
• B. $\sqrt{a-b}$
• C. $\sqrt{a^2-b^2}$
• D. $\sqrt{a^2+b^2}$

Answer 1

The correct option is C $\sqrt{a^2-b^2}$

Given equation of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

The equation of director circle to the hyperbola is $x^2+y^2=a^2-b^2$
$\therefore$ Radius $=\sqrt{a^2-b^2}$