Question

The length of the latus-rectum of the parabola x² − 4x − 8y + 12 = 0 is
(a) 4
(b) 6
(c) 8
(d) 10

Answer 1

(c) 8

Given:
x² − 4x − 8y + 12 = 0

$$\begin{gathered} \Rightarrow {\left(x-2\right)}^2-8y+8=0 \\ \Rightarrow {\left(x-2\right)}^2=8y-8=8\left(y-1\right) \end{gathered}$$

Let $X=x-2,Y=y-1$

∴ $X^2=8Y$

∴ Length of the latus rectum = 4a = 8 units