Question

The equation of the director circle of the hyperbola \[\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\] is______.

Options

• \[x^2+y^2=a^2+b^2\]

• \[x^{2}+y^{2}=a^{2}\]

• \[x^2+y^2=a^2-b^2\]

• \[x^2+y^2=2a^2\]

Answer 1

The equation of the director circle of the hyperbola \[\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\] is \[x^2+y^2=a^2-b^2\].

Explanation:

For a hyperbola, the director circle is \[x^2+y^2=a^2-b^2\], which differs from the ellipse because subtraction is used due to the nature of the hyperbola equation.