Quiz 8.2, #1
Point F is the given focus, (-3,2). The directrix, x=1, is given in blue. Notice that since the directrix is a vertical line, then the parabola must be HORIZONTALLY ORIENTED. We also know that by our definition of what a parabola is, the vertex is located an EQUAL DISTANCE between the focus and the directrix. This is point V. The distance from the focus to the vertex, f, is equivalent to the horizontal scale factor, a. Using these two pieces of information, we can find the vertical scale factor, b. Using these values and our general equation for a parabola, we can solve for y to come up with the two black equations. However, notice that these two black curves cross the directrix - which we know can never happen... so we need to include a horizontal "flip." The horizontally "flipped" parabola, shown in red, are the two equations we need.