Question

The length of the latus rectum of the conic $\frac{5}{r}=3-2\cos \theta$ is:

• A. $\frac{3}{5}$
• B. $\frac{5}{3}$
• C. $\frac{6}{5}$
• D. $\frac{10}{3}$

Answer 1

The correct option is D $\frac{10}{3}$

The general equation in polar coordinates is $\frac{l}{r}=1-e\cos \theta$
Compare with $\frac{5}{3r}=1-\frac{2}{3}\cos \theta$
Therefore, length of latus rectum is $2l=\frac{10}{3}$