Question

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

• A. $x^2+y^2=a^2$
• B. $x^2+y^2=b^2$
• C. $x^2+y^2=a^2+b^2$
• D. $x^2+y^2=a^2-b^2$

Answer 1

The correct option is D $x^2+y^2=a^2-b^2$

The Director circle of a hyperbola is defined as the locus of the point of intersection of two perpendicular tangents to the hyperbola. For any standard hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$,

The equation of Director circle is given by $x^2+y^2=a^2-b^2$

Hence the Director circle is a circle whose centre is same as centre of the hyperbola and the radius is $\sqrt{a^2-b^2}$

So correct option is $D$.