Question

The equation of the conic with $e=\frac{1}{2}$ and equation of directrix $r\cos \theta =2$ is:

• A. $r\cos \theta =r+1$
• B. $r\sin \theta =2(r+1)$
• C. $r\cos \theta =-2(r-1)$
• D. $r\sin \theta =2(r-1)$

Answer 1

Answer: (C)

$r\cos \theta =-2(r-1)$

Directrix of $\frac{l}{r}=1+e\cos \theta$ is $\frac{l}{r}=e\cos \theta$
by comparing we can get , $l=1$

Putting these values in dielectrix equation,

$\frac{1}{r}=1+\frac{1}{2}\cos \theta$

Therefore, equation of conic is $r\cos \theta =-2(r-1)$