Question

The equation of the directrix of the parabola $x^2+8y-2x=7$ is

• A. $y=3$
• B. $y=-3$
• C. $y=2$
• D. $y=0$

Answer 1

The correct option is A

$y=3$

Explanation for the correct option:

Finding the directrix:

Given, $x^2+8y-2x=7$

Simplifying the given equation,

$x^2-2x=7-8y$

Adding $1$ on both sides,

$$\begin{gathered} \Rightarrow x^2-2x+1=7+1-8y \\ \Rightarrow {(x-1)}^2=8-8y\mathbf{}\left[\because {(x-1)}^2=x^2-2x+1\right] \\ \Rightarrow {(x-1)}^2=8(1-y) \\ \Rightarrow {(x-1)}^2=-4\left(2\right)(y-1) \end{gathered}$$

The above equation is compared with the equation $X^2=-4aY$

Thus, we get the values of $X=x-1,a=2,Y=y-1$
Hence, the equation of the directrix of the parabola will be

$Y=a$

$$\begin{gathered} \Rightarrow y-1=2 \\ \Rightarrow y=3 \end{gathered}$$

Hence, option(A) is the correct answer.