Question

lf $\pi +\theta$ is the eccentric angle of a point on the ellipse $16x^2+25y^2=400$ then the corresponding point on the auxiliary 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 $(-5\cos \theta ,-5\sin \theta )$

$\frac{x^2}{25}+\frac{y^2}{16}=1$
The equation of auxiliary circle is $x^2+y^2=a^2$..............(for a general ellipse)
$\Rightarrow x^2+y^2=25$
The correspond point of point having eccentric angle $\pi +\theta$ is $\left(5cos\right(\pi +\theta ),5sin(\pi +\theta \left)\right)$
$i.e(-5cos\theta ,-5sin\theta )$