Question

The length of the latus rectum of the parabola $bx^2 - 4ay + dx + e = 0$ is

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

Answer 1

Answer: (D)

$\frac{4a}{b}$

Answer 2

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