The length of the latus-rectum of the ellipse, whose foci are (2, 5) and (2, –3) and eccentricity is 4/5, is

Question

The length of the latus-rectum of the ellipse, whose foci are (2, 5) and (2, -3) and eccentricity is \(\frac{4}{5},\) is

(1) \(\frac{6}{5}\)

(2) \(\frac{50}{3}\)

(3) \(\frac{10}{3}\)

(4) \(\frac{18}{5}\) 

Answer 1

Correct option is: (4) \(\frac{18}{5}\)  

\(2 \mathrm{be}=8\)

be = 4

 

\(\mathrm{b}\left(\frac{4}{5}\right)=4 \Rightarrow \mathrm{~b}=5\)

\(\because c^{2}=b^{2}-a^{2}\)

\(16=25-a^{2} \Rightarrow a=3\)

L.R. \(=\frac{2 \mathrm{a}^{2}}{\mathrm{~b}}=\frac{18}{5}\)