# What is the equation of the parabola with a focus at (3,-8) and a directrix of y= -5?

##### 2 Answers

The equation is

#### Explanation:

Any point

Therefore,

Squaring both sides

graph{(y+1/6(x-3)^2+39/6)(y+5)=0 [-28.86, 28.87, -14.43, 14.45]}

**The equation of parabola is**

#### Explanation:

Focus is at

between focus and directrix. Therefore,vertex is at

or at

So the equation of parabola is

vertex from directrix is

the vertex , so parabola opens downward and

graph{-1/6(x-3)^2-6.5 [-40, 40, -20, 20]}