Question

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

• A. $x^2+y^2=100$
• B. $x^2+y^2=28$
• C. $x^2+y^2=64$
• D. $x^2+y^2=36$

Answer 1

The correct option is C $x^2+y^2=64$

For any hyperbola of the form
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1,$
the auxiliary circle is $x^2+y^2=a^2$
Now for hyperbola$\frac{x^2}{64}-\frac{y^2}{36}=1,a=8\text{and}b=6$
Thus the auxiliary circle is $x^2+y^2=64$