What is the equation of a parabola with (4, 6) as its focus and y = 2 as its directrix
Whenever the focus lies above the directrix, the parabola turns "upward"
The vertex is
( x coordinate of the focus, [sum of y coordinate of the focus + numerical value of the directrix]/ 2 ) = ( 4, [6 + 2] / 2 ) = ( 4, 8/2) = (4, 4)
And we have the following form :
4p ( y - k) = (x - h)^2 where (h, k) is the vertex and "p" = y coordinate of the focus - y coordinate of the vertex = 6 - 4 = 2
So we have
4(2) ( y - 4) = ( x - 4)^2
8 (y - 4) = ( x - 4)^2
See the graph, here ;
https://www.desmos.com/calculator/o8jsbrmpgz