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

Answer: (C)

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 $=\sqrt{ a ^{2}- b ^{2}}$