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abruzzese [7]
2 years ago
13

Which is the equation of the parabola that

Mathematics
1 answer:
EastWind [94]2 years ago
5 0

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
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