Question

If $\theta +\pi$ is the eccentric angle of a point on the ellipse $16x^2+25y^2=400,$ then the corresponding point on the auxilary circle is

• A. $(-4\cos \theta ,-4\sin \theta )$
• B. $(-5\cos \theta ,-5\sin \theta )$
• C. $(4\cos \theta ,4\sin \theta )$
• D. $(5\cos \theta ,5\sin \theta )$

Answer 1

The correct option is B $(-5\cos \theta ,-5\sin \theta )$

Equation of the ellipse is:
$16x^2+25y^2=400$
$\Rightarrow \frac{x^2}{25}+\frac{y^2}{16}=1$

Any point $P(\theta +\pi )$ on the ellipse can be written as $\left(5\cos \right(\theta +\pi ),4\sin (\theta +\pi \left)\right)$ or $(-5\cos \theta ,-4\sin \theta )$

Hence corresponding point on the auxilary circle is $(-5\cos \theta ,-5\sin \theta )$