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fiasKO [112]
3 years ago
14

Write the equation of the parabola with vertex (3, 4) and focus (5, 4).

Mathematics
1 answer:
shtirl [24]3 years ago
3 0

Answer:

The equation of the parabola with vertex (3, 4) and focus (5, 4) will be:

  • \left(4\:-\:k\right)^2\:=\:8\left(3\:-\:h\right)\:

Step-by-step explanation:

Given

  • vertex (3, 4)
  • focus (5, 4)

As the y value of the vertex (3, 4) and the focus (5, 4) is the same.

So the parabola opens to the right.

Thus

The standard form of Parabola

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

Substituting vertex

\left(y\:-\:4\right)^2\:=\:4p\left(x\:-\:3\right)\:

As focus = (h + p, k)

5 = 3 + p

p = 2

so

\left(y\:-\:4\right)^2\:=\:4p\left(x\:-\:3\right)\:

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

\left(y\:-\:4\right)^2\:=\:8\left(x\:-\:3\right)\:

Therefore, the equation of the parabola with vertex (3, 4) and focus (5, 4) will be:

  • \left(y\:-\:4\right)^2\:=\:8\left(x\:-\:3\right)\:
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