Question

The length of latus rectum o f the parabola $4y^2 + 3x + 3y + 1 = 0$ is

• A. 44654
• B. 7
• C. 12
• D. 44624

Answer 1

Answer: (D)

44624

Answer 2

We have, $4 y^{2}+3 x+3 y+1=0$
$\Rightarrow 4 y^{2}+3 y=-3 x-1$
$\Rightarrow y^{2}+\frac{3}{4} y=-\frac{3}{4} x-\frac{1}{4}$
$\Rightarrow y^{2}+\frac{3}{4} y+\frac{9}{64}=-\frac{3}{4} x-\frac{1}{4}+\frac{9}{64}$
$\Rightarrow\left(y+\frac{3}{8}\right)^{2}=-\frac{3}{4}\left(x+\frac{7}{48}\right)$
$\therefore$ Length of latusrectum $=\frac{3}{4}$