Question

Which is the standard form of the equation of the parabola that has a vertex of (–4, –3) and a directrix of x = 2?

Answer 1

Standard form (y + 3)² = -24( x + 4).

Explanation:

Given : parabola that has a vertex of (–4, –3) and a directrix of x = 2.

To find : Which is the standard form of the equation of the parabola.

Solution :We have given that vertex of (–4, –3) and a directrix of x = 2.

Standard form eqauation of parabola its axis of symmetry is parallel to the x-axis : (y-k)² = 4p(x-h).

Where, vertex = (h,k) , directrix is x = h - p.

h = -4 , k= -3;

Directrix : 2 = -4 -p

Then p = -6

Now, plugging the values of vertex and p in standard form.

(y - (-3))² = 4(-6)( x - (-4)).

(y + 3)² = -24( x + 4).

Therefore, Standard form (y + 3)² = -24( x + 4).

Answer 2

Equation of the parabola is
`\left(y+3\right)^(2)=-24(x+4)`

Explanation:

We have to find the equation of a parabola with vertex is (-4,-3) and a directrix x=2.

As vertex is (-4,-3) that means parabola is in third quadrant.

So the standard formula of the parabola will be y²= -4px through origin (0,0).

But when a parabola is shifted from origin to the left of y axis so the equation will be (y-shifting form y axis)² = -4(distance between vertex and directrix)(x-shifting from x axis)

`\left\{y-(-3)\right\}^(2)=(-4* 6)\left\{x-(-4)\right\}`

`\left(y+3\right)^(2)=-24(x+4)`.