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Evaluate the vertical parabola

(y-2)² = 12(x-5)

Open Direction

Since our squared variable is y, our parabola has a horizontal opening.

Determine the vertex (h,k):

Our standard for for this parabola is (y - k)² = 4c(x - h)

Therefore, our vertex (h,k) = (5,2)

Determine focus:

From the right side of our standard form equation, we have 4c = 12

Divide each side by 4 to isolate c:

c = 3

The focus for a horizontal parabola is (h + c,k)

Substituting our values into this equation, we get:

Focus = (5 + 3,2)

Focus = (8,2)

Calculate the directrix:

The directrix equation for a horizontal parabola is x = c

Therefore, for c = 3, we have x = 3