Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1
+210 The parabola is the set of all points (x,y) that are equidistant from the focus and directrix.
So, using the distance formula, we have:
√[(x+5)2 + (y-5)2] = √[(x-x)2 + (y+1)2]
x2 + 10x + 25 + y2 - 10y + 25 = y2 + 2y + 1
x2 + 10x + 25 = 12y - 24
(x + 5)2 = 12(y - 2)
y - 2 = (1/12)(x + 5)2
y = (1/12)(x + 5)2 + 2
+210 The parabola is the set of all points (x,y) that are equidistant from the focus and directrix.
So, using the distance formula, we have:
√[(x+5)2 + (y-5)2] = √[(x-x)2 + (y+1)2]
x2 + 10x + 25 + y2 - 10y + 25 = y2 + 2y + 1
x2 + 10x + 25 = 12y - 24
(x + 5)2 = 12(y - 2)
y - 2 = (1/12)(x + 5)2
y = (1/12)(x + 5)2 + 2
