Question

how do I find the equation of a parabola with the directrix =-12

Answer 1

you need more information than just the directrix ....

Answer 2

sorry, it looks like the vertex is (-6,0)

Answer 3

then you want a setup such that the distance from any point to the focus is equal to the perpendicular distance to the directrix ....

Answer 4

so ... lets take a point (x,y) and compare distances

d1^2 = (-6-x)^2 + (0-y^2)

any point on the directrix is just (-12,y) sooo

d2^2 = (-12-x)^2 + (y-y^2)

set d1^2 = d2^2 and you have the equation

Answer 5

is that a directrix of x=-12? or y=-12?

Answer 6

lol, my ^2 on the ys are in the wrong spot ... assuming x=-12 is the directrix

(-6-x)^2 + (0-y)^2 = (-12-x)^2 + (y-y)^2

Answer 7

x=-12

Answer 8

then thats good lol

Answer 9

now its just a matter of expanding the squares and gathering like terms

(-6-x)^2 + (0-y)^2 = (-12-x)^2 + (y-y)^2

36+x^2+12x + y^2 = 144+x^2+24x+0^2

solve for x as a function of y

Answer 10

thanks, let me see if I can wrap my mind around all of this.

Answer 11

k, this isnt the only way to approach it ... but it works simply by using the definition of a parabola as being the set of all points that are equal distance from the focus, and perpendicular distance to the directrix