# How do you write the equation of the parabola in vertex form given vertex (5,-2) and focus (5,-4)?

##### 1 Answer

Jan 22, 2018

Equation is

#### Explanation:

As vertex is

as axis of symmetry passes through both and abscissa is common in both, equation of axis of symmetry is

and as directrix is perpendicular to it, its equation is of type

Now vertex is midway between directrix and focus and hence directrix is

The parabola is locus of a point

or

or

i.e.

graph{y(x^2-10x+8y+41)(x-5)((x-5)^2+(y+2)^2-0.03)((x-5)^2+(y+4)^2-0.03)=0 [-5.04, 14.96, -7.16, 2.84]}