Answer :
Answer:
The equation of the parabola will be:
- [tex]\:y^2=12x[/tex]
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 .
[tex]p=3-0[/tex]
[tex]p=3[/tex]
Substitute in the known values for the variables into the equation
[tex]\left(y-k\right)^2=4p\left(x-h\right)[/tex]
[tex]\left(y-0\right)^2=4\left(3\right)\left(x-0\right)[/tex]
[tex]\:y^2=12x[/tex]
Therefore, the equation of the parabola will be:
- [tex]\:y^2=12x[/tex]