Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -7).

The standard form of the equation of a parabola gives details of the vertex and focus coordinates

The standard form of the equation of the parabola is x² = -28·y

The reason why the equation is correct is given as follows;

The known parameters of the parabola are;

The location of the vertex = The origin, (0, 0)

The location of the focus of the parabola = (0, -7)

Solution:

The equation of the parabola can be expressed as follows;

(x - h)² = 4·p·(y - k)

Where;

(h, k) = The coordinates of the vertex

(h, k + p) = The coordinates of the focus

By comparison with the given coordinates, we have;

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

h = 0, k = 0

(h, k + p) = The coordinates of the focus = (0, -7)

k + p = -7

0 + p = -7

p = -7

The standard form of the equation of the parabola is therefore;

(x - 0)² = 4 × (-7) × (y - 0)

x² = -28·y

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