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Write an equation of the parabola with the given focus and vertex Focus:(2,4) vertex (2,0 )

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Answer to a math question Write an equation of the parabola with the given focus and vertex Focus:(2,4) vertex (2,0 )

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Bud

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92 Answers

1. Identify the vertex

(h,k) = (2,0)

.
2. Identify the focus

(h,k + p) = (2,4)

.
3. Determine the value of

: since the focus is $4$ units above the vertex,

p = 4

.
4. Substitute the values into the standard form of a parabola

(x - h)^2 = 4p(y - k)

(x - 2)^2 = 4 \cdot 4 \cdot (y - 0)

5. Simplify the equation:

(x - 2)^2 = 16y

Thus, the equation of the parabola is

(x - 2)^2 = 16y

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Write an equation of the parabola with the given focus and vertex Focus:(2,4) vertex (2,0 )

Answer to a math question Write an equation of the parabola with the given focus and vertex Focus:(2,4) vertex (2,0 )

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