Question

Write the standard form of the equasion of the parabola with the vertex at (0,0) and the directrix x=-3/4

Answer 1

Since the directrix is x = -3/4, a vertical line, the axis of symmetry of this parabola is horizontal and is the x-axis.

In this case (horiz. axis of sym.), 4p(x-0) = (y-0)^2, or 4px = y^2. The horiz. distance of the directrix from the vertex is 3/4, and so p = 3/4.

Rewriting 4px = y^2 using p = 3/4, we get 4(3/4)x = y^2, or 3x = y^2. This last equation is the equation of the parabola.