Question

Find the length of latus rectum of the ellipse $4x^2+9y^2+8x+36y+4=0$.

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{4}{3}$
• D. $\frac{8}{3}$

Answer 1

The correct option is D $\frac{8}{3}$

$4x^2+9y^2+8x+36y+4=0$
$\Rightarrow 4(x^2+2x)+9(y^2+4y)=-4$
$\Rightarrow 4(x^2+2x+1)+9(y^2+4y+4)=-4+4+36$
$\Rightarrow 4(x+1{)}^2+9(y+2{)}^2=36$
$\Rightarrow \frac{(x+1{)}^2}{9}+\frac{(y+2{)}^2}{4}=1$
$\therefore a^2=9,b^2=4$
Hence length of latus rectum is $=\frac{2b^2}{a}=\frac{8}{3}$