Which is the equation of a parabola with a directrix at y = −3 and a focus at (5, 3)? y = one twelfth(x − 5)2 y = −one twelfth(x − 5)2 y = one twelfth(x + 5)2 y = −one twelfth(x + 5)2

The answer to your question is   y = 1/12 (x - 5)²

Step-by-step explanation:

Data

directrix   y = -3

focus       (5, 3)

Process

1.- Graph the directrix and focus to determine if the parabola is vertical or horizontal.

From the graph we know that it is a vertical parabola with equation

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

2.- From the graph we know that p = 3 because the distance from the focus to the directrix is 6 and p = 6/2.

3.- The vertex (5, 0)

4.- Substitution

                 (x - 5)² = 4(3)(y - 0)

5.- Simplification

                (x - 5)² = 12y

6.- Result

                y = 1/12 (x - 5)²

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step-by-step explanation:

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step-by-step explanation: