Find an equation of a parabola with a vertex at the origin and directrix y = -2.5

Solution:

Given, vertex (h,k) = (0, 0)

Directrix y = -2.5

Focus = (0, 2.5)

The parabola is opening up, as its directrix is y = -2.5

The general equation of the parabola in vertex form is given by

(x - h)² = 4a (y - k)

Where, (h,k) is the vertex.

a = distance between vertex and focus.

a = 0 - (-2.5)

a = 2.5

Here, a = 2.5, h = 0 and k = 0

So,(x - 0)² = 4(2.5) (y - 0)

x² = 10y

Therefore, the equation of parabola is x² = 10y.

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Find an equation of a parabola with a vertex at the origin and directrix y = -2.5

Summary:

An equation of a parabola with a vertex at the origin and directrix y = -2.5 is x² = 10y.