Page 83 - Calculus for the Clueless, Calc II

Example 14—

Find the equation of the parabola with focus (1,3), directrix x = 11.

Draw F and the directrix. Your sketch should match the figure. Vertex is halfway between the x numbers. So x
2
= (11 + 1)/2 = 6; V = (6,3); c = the distance between V and F = 5. The equation is (y - 3) = -4c(x - 6) = -20(x -
6). Remember, the minus sign comes from the shape, and c is always positive for these problems.