Question

The centre, vertex, focus of a conic are $(0,0),(0,5),(0,6)$. Its length of latus rectum is

• A. $\frac{11}{5}$
• B. $\frac{7}{5}$
• C. $\frac{14}{5}$
• D. $\frac{22}{5}$

Answer 1

The correct option is D $\frac{22}{5}$

Given centre vertex and focus of the conic are $C(0,0),A(0,5)$ and $(0,6)$ respectively
$\Rightarrow a=5,ae=6\Rightarrow e=\frac{6}{5}$
Thus $b^2=a^2(e^2-1)=11$
Therefore, length of latus rectum is $=\frac{2b^2}{a}=\frac{22}{5}$
Hence, option 'D' is correct