What is the standard form of the equation of the parabola with a directrix at x=-8 and a focus at (-7,3)?
The directrix is x = 8 the focus S is (-7, 3), in the negative direction of x-axis, from the directrix..
Using the definition of the parabola as the locus of the point that is equdistant from the directrix and the focus, its equation is
as the parabola is on the focus-side of the directrix, in the negative x-direction.
Squaring, expanding and simplifying, the standard form is.
The axis of the parabola is y = 3, in the negative x-direction and the vertex V is (1/2, 3). The parameter for size, a = 15/2.,