Question

For the hyperbola $\frac{x^2}{64}-\frac{y^2}{36}=1$, the equation of director circle is

• A. $x^2+y^2=100$
• B. $2x^2+2y^2=100$
• C. $x^2+y^2=28$
• D. $x^2-y^2=100$

Answer 1

The correct option is C $x^2+y^2=28$

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 $x^2+y^2=a^2-b^2$

Here the given hyperbola is $\frac{x^2}{64}-\frac{y^2}{36}=1$,

Here $a=8$ and $b=6$

So equation of the director circle will be $x^2+y^2=(8{)}^2-(6{)}^2$

$\Rightarrow x^2+y^2=28$

Correct option is $C$.