How do you write the equation of the parabola in vertex form given Vertex (2,4), Focus (2,6)?

1 Answer
bp
Jul 8, 2017

#(x-2)^2 = 8(y-4)#

Explanation:

Standard equation of a vertical parabola with vertex (h,k) is #(x-h)^2 =4p(y-k)# where p is the distance of the focus from the vertex. In the present case vertex is (2,4). Since the focus is at (2,6), the distance of the focus from vertex , that is 'p' would be 6-4= 2 units.

The required equation of the parabola thus can be written as :

#(x-2)^2 = 8(y-4)#

This is shown in the figure below:
enter image source here

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