Find the equation of the parabola determined by the given information vertex at the origin, focus at (0,-5)
Since the vertex is at the origin and the focus is at (0,-5), we know that the parabola is opening downwards. The vertex form of the equation of a parabola with vertex at (h, k) is given by:
(y - k) = 4a(x - h)
Since the vertex is at the origin (0,0), the equation simplifies to:
y = 4ax
To find the value of 'a', we need to consider the distance between the vertex and the focus, which is equal to the absolute value of the value of 'a'. In this case, the distance is 5 units, so a = -5.
Therefore, the equation of the parabola is:
y = -20x