given the directrix of y = 6 and focus of (0, 4), which is the equation of the parabola?

The answer to your question is:    

x² = -8(y - 4)     or general equation      x² + 8y - 32 = 0

Step-by-step explanation:

Data

Directrix = y = 6

Focus = (0, 4)

p = 2

Formula

Vertical parabola equation (x - h)² = - 4p (y - k)

Process (see the picture attached)

                                            (x - 0)² = - 4(2) (y - 4)             Substitution

                                            x² = -8(y - 4)                           Simplify

                                            x² = -8y + 32

                                           x² + 8y - 32 = 0

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explanation: