Derive the equation of the parabola with a focus at (0, -4) and a directrix of y=4

There are several parameters that can be used to determine the equation of a parabola

The equation of the parabola i

The given parameters are given as:

---- focus

--- directrix

The equation of the parabola is calculated using:

So, we have:

Square both sides

Evaluate all exponents

Cancel out common terms

Collect like terms

Make y the subject

Divide both sides by 16

Hence, the equation of the parabola i

Read more about parabolas at:

link

C

Step-by-step explanation:

The focus and directrix are equidistant from any point (x, y) on the parabola.

Using the distance formula

= | y - 4 |

= | y - 4 |

Square both sides

x² + (y + 4)² = (y - 4)² ← expand parenthesis on both sides

x² + y² + 8y + 16 = y² - 8y + 16

Subtract y² - 8y + 16 from both sides

x² + 16y = 0 ( subtract x² from both sides )

16y = - x² ( divide both sides by 16 )

y = - x², or

f(x) = - x² → C

2

step-by-step explanation:

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