Question

For the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$, the point $(5\cos \theta ,5\sin \theta )$ lies on its:

• A. director circle
• B. auxiliary circle
• C. focus
• D. None of these

Answer 1

The correct option is B auxiliary circle

Auxiliary circle of ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ is $x^2+y^2=25$

$(5\cos \theta ,5\sin \theta )$ lies on $x^2+y^2=25$.

Hence, option B.