Homework Soursex228y3 I get that the 4p8 which p2but in the formula it say
(x+2)^2=8(y-3). I get that the 4p=8 which = p=2....but in the formula it says directrix is -p which would make it -2...but the dirextrix is y=1..Please explain and show..Thank You
Solution
You calculated the p correctly, but this tells you how far to move from the vertex. As the expression is (x+2)^2=8(y-3), from x + 2, we get that x+2 = 0, so x = -2; from y - 3, we get that y - 3 = 0, so y = 3 Thus, the vertex is at (-2, 3). To get the directrix, then, we must calculate using the y coordinate of the vertex, 3 + - p = 3 + -2 = 1 Thus, the directrix is y = 1. The focus will also be relative to the vertex and be at (-2, 3 + p ) = (-2, 5) From (x+2)^2=8(y-3), (x+2)^2/8 =y-3, or (x+2)^2/8 + 3 = y I invite you to plot this function and see the reasonableness of this solution. Let x vary from -12 to 8.
