Algebra
posted by Tim .
Can someone tell me if I am right?
I need to find the equation of a parabola. I am not sure if this is the correct way or if I have the correct answer.
Vertex at origin, focus is at (0,3)
Equation of parabola
vertex (0,0) focus (0,3)
focus (h,k+p)
(0,0+3)
y=03
directrix y=3
a=(1/4)(p)
a=(1/4(3))=(1/12)
a=(1/12) h=0 k=0
y=(1/12)(x0)^2+0
my answer is: y=(1/12)(x^2)+0

shouldn't your parabola open upwards ?
your 1/12x^2.... makes it open down.
I do it this way:
let P(x,y) be any point on the parabola
by definition, the distance from P to the focal point is equal to the distance to the directrix >
√(x^2 + (y3)^2) = √(y+3)^2)
square both sides, and simplify to get
y = (1/12)x^2