# What is the equation of the parabola with a focus at (10,19) and a directrix of y= 22?

Equation of parabola is

This is a regular parabola with a squared x part since the line is perpendicular to the axis of symmetry.

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The equation of the parabola with a focus at (10, 19) and a directrix of y = 22 is:

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

where:

- (h, k) is the coordinates of the vertex,
- p is the distance between the vertex and the focus (and also the distance between the vertex and the directrix).

In this case:

- The vertex is the midpoint between the focus and the directrix, so (h, k) = (10, 20.5),
- p = 20.5 - 22 = -1.5.

Substituting the values into the equation:

[ (x - 10)^2 = 4(-1.5)(y - 20.5) ]

Simplify the equation to get the final equation of the parabola.

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