Find the equation of the parabola with vertex at (0,0) and focus at (0,3).
In the equation y = a·x2, the value 'a' has the value '1/(4f)', where 'f' is the focal length.
Since the distance form (0,0) to (0,3) is 3, the focal length = 3 ---> f = 3 ---> a = 1/(4·3) ---> a = 1/12
---> y = (1/12)·x2
Find the equation of the parabola with vertex at (5,4) and focus at (-3, 4).
In the equation x - h = a(y - k)2, (h,k) is the vertex ---> h = 5 and k = 4
Since the focal length is 8: f = 8 ---> a = 1/(4·8) ---> a = 1/32
Since the parabola opens to the left, a must be negative ---> a = -1/32
---> x - 5 = (-1/32)(y - 4)2