Question

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

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

Answer 1

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

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 $D$.