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

Jul 8, 2017

${\left(x - 2\right)}^{2} = 8 \left(y - 4\right)$

#### Explanation:

Standard equation of a vertical parabola with vertex (h,k) is ${\left(x - h\right)}^{2} = 4 p \left(y - k\right)$ 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 :

${\left(x - 2\right)}^{2} = 8 \left(y - 4\right)$

This is shown in the figure below: