10.8 Polar Equations of Conics

In this section, we are finding the polar equations of conics and graphing them on polar graphs. In this example, we are given the type of conic (parabola), the eccentricity (1), and the directrix (y=-2). With a horizontal directrix below the origin, we can tell that the equation's denominator will be (1-esinØ). The directrix is also 2 units away from the focus [which is always at (0,0) for these problems], so we know that p is 2. The bottom row of this picture displays how to insert those numbers and find the final equation (boxed on the right).