Question

What is the equation of the auxiliary circle of the ellipse \[\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\] where a > b?

Options

• \[x^2+y^2=b^2\]

• \[x^2+y^2=a^2+b^2\]

• \[x^2+y^2=a^2\]

• \[x^2+y^2=2a^2\]

Answer 1

\[x^2+y^2=a^2\]

Explanation:

The auxiliary circle of an ellipse is drawn with the semi-major axis \(a\) as its radius, giving \[x^2+y^2=a^2\].