Question

Which is the equation of the parabola that

Answer 1

Answer:

The equation of the parabola will be:

• $\:y^2=12x$

Step-by-step explanation:

The vertex  (h, k)  is halfway between the directrix and focus.

Find the  x  coordinate of the vertex using the formula

x = (x-coordinate of focus + directrix)/2

 = (3-3)/2

 = 0/2

 =0

The  y -coordinate will be the same as the y-coordinate of the focus.

so the vertex will be: (0, 0)

Finding the distance from the focus to the vertex

The distance from the focus to the vertex and from the vertex to the directrix is |p|.

Subtract the  x  coordinate of the vertex from the x -coordinate of the focus to find  p .

$p=3-0$

$p=3$

Substitute in the known values for the variables into the equation

$\left(y-k\right)^2=4p\left(x-h\right)$

$\left(y-0\right)^2=4\left(3\right)\left(x-0\right)$

$\:y^2=12x$

Therefore, the equation of the parabola will be:

• $\:y^2=12x$