Question

If the equation of parabola is$x^2=-8y$, then equation of directrix , length of latus rectum are

• A. $y=–(9/8),8$
• B. $y=2,8$
• C. $y=–(9/4),9$
• D. None of these

Answer 1

The correct option is B

$y=2,8$

Explanation for the correct options:

Step 1: Comparing the equation with standard form

The given equation of parabola is $x^2=-8y$

Now comparing with the standard form $x^2=-4ay$ we get $a=2$,

Step 2: Find the equation of directrix

For a given equation of parabola $x^2=-4ay$ the equation of directrix is $y=a$

Therefore the equation of the directrix of the parabola $x^2=-8y$ is

$$\begin{gathered} y=a \\ \Rightarrow y=2\mathbf{}\left[\because a=2\right] \end{gathered}$$

Step 3: Find the length of Latus rectum

For a given equation of parabola $x^2=-4ay$ the length of latus rectum is $4a$

Therefore the length of latus rectum of the parabola $x^2=-8y$ is $8$

Hence, option (B) is correct i.e. $y=2,8$