Question

The equation of auxiliary circle of the hyperbola $\frac{x^2}{4}-\frac{y^2}{9}=1$ is

• A. $x^2+y^2=4$
• B. $x^2+y^2=9$
• C. $x^2+y^2=13$
• D. $x^2+y^2=5$

Answer 1

Answer: (A)

The hyperbola is $\frac{x^2}{4}-\frac{y^2}{9}=1$


Auxilliary circle is the circle between the two curves of hyperbola.
$\therefore (a,0)$ and $(-a,0)$ touches the circle with centre (0, 0)
$\therefore$ Equation of circle is
${\left(x-0\right)}^2+{\left(y-0\right)}^2={\left(\sqrt{{\left(a-0\right)}^2+{\left(0-0\right)}^2}\right)}^2$
$\Rightarrow x^2+y^2=a^2$
So, $x^2+y^2=4$ $(\because a=2)$