Find the equation of auxiliary circle to the ellipse 9x² + 16y² = 144.

Given ellipse 9x² + 16y² = 144
$\frac{{\mathrm{x}}^2}{16}+\frac{{\mathrm{y}}^2}{9}=1 where a^2=16,b^2=9$

Now equation of auxiliary circle is $$\begin{gathered} x^2+y^2=a^2 \\ \Rightarrow x^2+y^2=16 \end{gathered}$$