Write the equation of a parabola with focus (2,2) and directrix y = -4.
+128631 focus = ( 2,2)
directix = y = -4
The directrix is below the fosus so this parabola will turn upward
The form we are looking for is
4p ( y - k) = (x - h)^2
(h , k) is the vertex .....this is given by ( x coordinate of focus , ( y coordinate of focus + directrix) / 2) =
(2 , ( 2 +-4) / 2) = ( 2 ,-2/2) = (2, -1)
p = the distance between the fcus and the vertex = y coordinate of focus - y coordinate of vertex =
2 - -1 = 3
So....the equation is
4(3) ( y - - 1) = ( x -2)^2 → 12 (y + 1) = ( x - 2)^2
Here's the graph : https://www.desmos.com/calculator/xik9fowbq0
