Hey bot ,Find an equation of a para bola with the vertex at the origin of Directrix y=-3.5
To find the equation of a parabola with the vertex at the origin and a directrix at y = -3.5, we need to determine the equation in standard form: (x-h)^2 = 4p(y-k), where (h,k) represents the coordinates of the vertex and p represents the distance between the vertex and the focus.
In this case, since the vertex is at the origin (0,0), we have h = 0 and k = 0. The directrix is y = -3.5, which means the distance between the vertex and the directrix is p = 3.5.
Substituting the obtained values into the standard equation, we get:
(x-0)^2 = 4(3.5)(y-0)
Simplifying further:
x^2 = 14y
Therefore, the equation of the parabola with the given vertex and directrix is x^2 = 14y.