What is the equation of a parabola with focus (0,-8) and directrix y=8?

y = - x²

Step-by-step explanation:

Any point (x, y) on the parabola is equidistant from the focus and the directrix.

Using the distance formula

= | y - 8 |

Square both sides

x² + (y + 8)² = (y - 8)² ← expand parenthesis on both sides

x² + y² + 16y + 64 = y² - 16y + 64 ( subtract y² - 16y + 64 from both sides )

x² + 32y = 0 ( subtract x² from both sides )

32y = - x² ( divide both sides by 32 )

y = - x²

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation:

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step-by-step explanation:

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