Which of the following equations below represent the standard form of the equation of a parabola with vertex at (0,-5) and focus at (0,-9).

Solution:

Given, vertex of parabola is (0, -5)

Focus of parabola is (0, -9)

We have to find the equation of the parabola.

The general form of equation of parabola is given by

(x - h)² = -4a(y - k)

Here, h = 0

k = -5

So, (x - 0)² = -4a(y - (-5))

x² = -4a(y + 5)

We know, the distance between the focus and the vertex is a

So, a = |-9 - (-5)|

a = |-9 + 5|

a = |-4|

a = 4

Put a = 4 in the above equation,

x² = -4(4)(y + 5)

x² = -16(y + 5)

Therefore, the equation of parabola is x² = -16(y + 5).

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Which of the following equations below represent the standard form of the equation of a parabola with vertex at (0,-5) and focus at (0,-9).

Summary:

The equation that represents the standard form of the equation of a parabola with vertex at (0,-5) and focus at (0,-9) is x² = -16(y + 5)