+164 What is the equation of a parabola with (−2, 4) as its focus and y = 6 as its directrix?
+128408
Since the focus is below the directrix, this parabola turns downward
The vertex is given by ( -2, [ 6 + 4] / 2) = ( -2, 5)
And p = (5 - 6) = -1
So the equation becomes
4p( y - k) = (x - h)^2 where (h, k) is the vertex and p = -1
So we have
4(-1) (y - 5) = ( x + 2) ^2
-4(y - 5) = ( x + 2) ^2
Here is the graph : https://www.desmos.com/calculator/8iug8y6j5h
+128408
Since the focus is below the directrix, this parabola turns downward
The vertex is given by ( -2, [ 6 + 4] / 2) = ( -2, 5)
And p = (5 - 6) = -1
So the equation becomes
4p( y - k) = (x - h)^2 where (h, k) is the vertex and p = -1
So we have
4(-1) (y - 5) = ( x + 2) ^2
-4(y - 5) = ( x + 2) ^2
Here is the graph : https://www.desmos.com/calculator/8iug8y6j5h
