Question

Write the equation of the parabola with a focus (-2,4) and directrix y = 0.

Answer 1

y=0 means sideways from the usual orientation. The definition of a parabola is equal distances of (x,y) to the focus and the directrix.  We equate squared distance:

(x + 2)² + (y - 4)² = (y - 0)²

x² + 4x + 4 + y² - 8y + 16 = y²

x² + 4x + 20 = 8y

We could divide by 8 to get y= something but let's just skip the fractions and answer

Answer: 8y = x² + 4x + 20