What is the vertex form of the equation of the parabola with a focus at (31,24) and a directrix of y=23 ?
1 Answer
May 28, 2017
y=1/2(x^2-62x+1008)
Explanation:
Look at the graph
The parabola is facing upwards, hence
(x-h)^2=4a(y-k)
Here
Vertex lies exactly at the middle of focus and directrix.
y coordinate of the vertex
Vertex
(x-31)^2=4xx0.5xx(y-23.5)
x^2-62x+961=2y-47
2y-47=x^2-62x+961
2y=x^2-62x+961+47
y=1/2(x^2-62x+1008)