Conic Sections Question 252

Question: Latus rectum of ellipse $ 4x^{2}+9y^{2}-8x-36y+4=0 $ is

[MP PET 1989]

Options:

A) 8/3

B) 4/3

C) $ \frac{\sqrt{5}}{3} $

D) 16/3

Show Answer

Answer:

Correct Answer: A

Solution:

The ellipse is $ 4{{(x-1)}^{2}}+9{{(y-2)}^{2}}=36 $

Therefore, latus rectum $ =\frac{2b^{2}}{a}=\frac{2.4}{3}=\frac{8}{3} $ .