What is the equation of the parabola with vertex (-5, 4) and focus (-2, 4)?

Question

What is the equation of the parabola with vertex (-5, 4) and focus (-2, 4)?

Answer 1

The y value of the vertex and the focus is the same.

The parabola opens to the right.

(y - k)² = 4p(x - h)         standard form

(y - 4)² = 4p(x - (-5))     substitute vertex

(y - 4)² = 4p(x + 5)

focus = (h + p, k)

(-2, 4) = (-5 + p, k)

-2 = -5 + p

3 = p

Can you complete the form?

Answer 2

The vertex (h,k) and focus lie on the axis of the parabola, so the axis is horizontal .  An equation of the parabola is (y-k)² = 4p(x-h).

 

                                                            (y-4)² = 4p(x+5)

 

Since the focus lies 3 units to the right of the vertex, the parabola opens rightward and p = 3.

 

Equation of parabola:  (y-4)² = 12(x+5).