# What is the vertex form of the equation of the parabola with a focus at (55,45) and a directrix of #y=47 #?

##### 1 Answer

Mar 31, 2018

#### Explanation:

Parabola is locus of a point which moves so that its distance from a given point calld focus and a given line ccalled directrix is always constant.

Let the point be

Hence equaion of parabola is

or

or

i.e.

Hence parabola's equation is

graph{((x-55)^2-184+4y)(y-47)((x-55)^2+(y-45)^2-0.1)=0 [35, 74.99, 35.02, 55.02]}