Question

A parabola is given by the equation y2 = -24x. The equation of the directrix of the parabola is

Answer 1

Answer:

$x=6$

Step-by-step explanation:

We have been given an equation of a parabola $y^2=-24x$. We are asked to find the equation of directrix of the given parabola.

First of all, we will convert our given equation in standard form of right-left opening parabola: $4p(x-h)=(y-k)^2$, where, $|p|$ represents focal length and (h,k) is vertex of parabola.

We can rewrite our given equation as:

$-24x=y^2$

$4(-6)(x-0)=(y-0)^2$

Since our given parabola has a $y^2$ term, so it will be symmetric about x-axis.

The vertex of parabola is (0,0) and focal length is 6.

We know that equation of directrix of right-left opening parabola is $x=h-p$.

$x=0-(-6)$

$x=0+6$

$x=6$

Therefore, the equation of the directrix of our given parabola is $x=6$.

Answer 2

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. 
y^=-12x
**
y^2=-12x
This is an equation of a parabola with a horizontal axis of symmetry. 
Its standard form: (y-k)^2=4p(x-h), with (h,k) being the (x,y) coordinates of the vertex.
For given equation:

Vertex(0,0) 
4p=12
p=3
Focus:(-3,0)
Directrix: x=3
see the graph below as a visual check on the answers:
..
y=±(-12x)^.5