Question

The equation of director circle of hyperbola is $\frac{x^2}{36}-\frac{y^2}{25}=1$ is

• A. $x^2+y^2=4$
• B. $x^2+y^2=11$
• C. $x^2-y^2=4$
• D. $x^2+y^2=61$

Answer 1

Answer: (B)

$x^2+y^2=11$

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 $\frac{x^2}{36}-\frac{y^2}{25}=1$,

Here $a=6$ and $b=5$

So equation of the director circle will be $x^2+y^2=(6{)}^2-(5{)}^2$

$\Rightarrow x^2+y^2=11$

Correct option is $B$.