In Example 2, change −8x to −20x.

Data from Example 2

If the focus is to the left of the origin, with the directrix an equal distance to the right, the coefficient of the x-term is negative. This tells us that the parabola opens to the left, rather than to the right, as in the case when the focus is to the right of the origin. For example, the parabola y² = −8x has its vertex at the origin, its focus at (−2, 0), and the line x = 2 as its directrix. We determine this from the equation as follows:

Because p = −2, we find the focus is (−2, 0) the directrix is the line x = −(−2), or x = 2 The parabola opens to the left, as shown in Fig. 21.45.

y = -8x 4p = -8, P = -2