Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1

Guest Feb 24, 2020

#1**+1 **

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

TacoBell Feb 24, 2020

#1**+1 **

Best Answer

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

TacoBell Feb 24, 2020