Question

The length of the latus rectum of the parabola $b{x}^2-4ay+dx+e=0$ is

• A. $\frac{a}{b}$
• B. $4a$
• C. $\frac{4b}{a}$
• D. $\frac{4a}{b}$

Answer 1

Answer: (D)

$b{x}^2-4ay+dx+e=0$
$\Rightarrow x^2+\frac{dx}{b}+\frac{d^2}{4b^2}-\frac{d^2}{4b^2}=\frac{4ay}{b}-\frac{e}{b}$
$\Rightarrow {\left(x+\frac{d}{2b}\right)}^2=\frac{4ay}{b}+\frac{d^2}{4b^2}-\frac{e}{b}$
$=\frac{4a}{b}\left[y+\frac{d^2}{16ab}-\frac{e}{4a}\right]$
On comparing with general equation of parabola $(X+x{)}^2=4a(Y+y)$, we have
Length of latus rectum $=\frac{4a}{b}$