can someone help me with algebra 2?

Question

the directrix of the parabola 12(y+3)=(x-4) to the 2 power has the equation y=-6. find the coordinates of the focus of the parabola

Answer 1

The equation of the given parabola is in "conics form," which is:

 

4p(y - k) = (x - h)², where (h, k) is the vertex of the parabola, and p is the distance between the vertex and the focus

 

This is a "right-side up" parabola, so the focus is above the vertex.

 

In our problem, 4p = 12 or p = 3

 

The vertex is (4, -3)

 

The focus is 3 units above the vertex, or at (4, 0)