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

Answer:

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

Step-by-step 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

Answer:

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

Step-by-step 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)

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

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