Question

The length of the latus-rectum of the parabola 4y² + 2x − 20y + 17 = 0 is
(a) 3
(b) 6
(c) 1/2
(d) 9

Answer 1

(c) 1/2

Given:
4y² + 2x − 20y + 17 = 0

$$\begin{gathered} \Rightarrow y^2+\frac{x}{2}-5y+\frac{17}{4}=0 \\ \Rightarrow {\left(y-\frac{5}{2}\right)}^2+\frac{x}{2}-2=0 \\ \Rightarrow {\left(y-\frac{5}{2}\right)}^2=-1\left(\frac{x}{2}-2\right) \\ \Rightarrow {\left(y-\frac{5}{2}\right)}^2=\frac{-1}{2}\left(x-4\right) \end{gathered}$$

Let $X=x-4,Y=y-\frac{5}{2}$

$\therefore Y^2=\frac{-X}{2}$

∴ Length of the latus rectum = 4a = $\frac{1}{2}$ units