Geometry question - parabola! (giving points to best answer)?
A parabola has a focus of F(1,3) and a directrix of y=2.
P(x,y) represents any point on the parabola, while D(x,2) represents any point on the directrix.
What are the steps required to find the equation of the parabola?
- PopeLv 73 years agoFavorite Answer
Notice that PD is the distance from P to the directrix. The parabola is the locus of all points equidistant from the focus and the directrix.
PF = PD
√[(x - 1)² + (y - 3)²] = |y - 2|
(x - 1)² + (y - 3)² = (y - 2)²
x² - 2x + 1 + y² - 6y + 9 = y² - 4y + 4
x² - 2x - 2y + 6 = 0