Question

The equation of director circle of $\frac{x^2}{64}-\frac{y^2}{49}=1$ is

• A. $x^2+y^2=15$
• B. $x^2+y^2=64$
• C. $x^2+y^2=18$
• D. $x^2+y^2=10$

Answer 1

The correct option is A $x^2+y^2=15$

Equation of hyperbola is $\frac{x^2}{64}-\frac{y^2}{49}=1$

Here $a=8,b=7$

Equation of director circle for hyperbola is

$x^2+y^2=a^2-b^2{x}^2+y^2=64-49x^2+y^2=15$

Hence, option A is correct.