Please find an parabola equation with vertex (2,2) and directrix =9

Question

Please find an parabola equation with vertex (2,2) and directrix =9

Thanks!

Answer 1

As long as the directrix is y=9 here's what you do. 

 

The equation you're working with is:

(x-h)²=4p(y-k)

 

You have (h,k) because of the vertex given, but you need to find 'p' using the directrix. It is important to know that your parabola does not cross the directrix. The directrix for this equation is above the vertex so your parabola opens down. The distance between your vertex and directrix is 7. The vertex is always in the middle of your directrix and focus. The focus of a parabola always lands within the parabola, so for this equation it is -7 from the vertex. 

 

Remember that your vertex signs change when you put them into the equation, so your equation is:

(x-2)²=(4)(-7)(y-2)

(x-2)²=-28(y-2)

 

because your parabola opens down, you have to make sure the equation is negative.