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

Answer:CStep-by-step explanation:The focus and directrix are equidistant from any point (x, y) on the parabola.Using the distance formula[tex]\sqrt{(x-0)^2+(y+4)^2}[/tex] = | y - 4 |[tex]\sqrt{x^2+(y+4)^2}[/tex] = | y - 4 |Square both sidesx² + (y + 4)² = (y - 4)² ← expand parenthesis on both sidesx² + y² + 8y + 16 = y² - 8y + 16Subtract y² - 8y + 16 from both sidesx² + 16y = 0 ( subtract x² from both sides )16y = - x² ( divide both sides by 16 )y = - [tex]\frac{1}{16}[/tex] x², orf(x) = - [tex]\frac{1}{16}[/tex]x² → C