Question

The equation of the director circle of the hyperbola $\frac{x^2}{16}-\frac{y^2}{4}=1$ is given by:

• A. $x^2+y^2=16$
• B. $x^2+y^2=4$
• C. $x^2+y^2=20$
• D. $x^2+y^2=12$

Answer 1

The correct option is D $x^2+y^2=12$

Equation of director circle of hyperbola, $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is given by $x^2+y^2=a^2-b^2$

Hence director circle of $\frac{x^2}{16}-\frac{y^2}{4}=1$ is $x^2+y^2=16-4=12$