Question

The diametre of director circle of hyperbola $\frac{x^2}{25}-\frac{y^2}{16}=1$

• A. $3$
• B. $9$
• C. $6$
• D. $2$

Answer 1

Answer: (C)

$6$

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 $\frac{x^2}{25}-\frac{y^2}{16}=1$,

Here $a=5$ and $b=4$

So equation of the director circle will be $x^2+y^2=(5{)}^2-(4{)}^2$

$\to x^2+y^2=9$

Hence the radius of the director circle is $\sqrt{9}=3$. So the diameter will be $6$.

So correct option is $C$.