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  4. The equation to the auxiliary circle of the ellipse 16 x2+9 y2=144 is

Q. The equation to the auxiliary circle of the ellipse $16 x^{2}+9 y^{2}=144$ is

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Solution:

$16 x^{2}+9 y^{2}=144 $
$\Rightarrow \frac{x^{2}}{9}+\frac{y^{2}}{16}=1$
$\therefore$ the auxiliary circle is $x^{2}+y^{2}=16$

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