What is the vertex form of the equation of the parabola with a focus at (52,48) and a directrix of #y=47 #?
The vertex form of the equation of a parabola is:
We know that the vertex is equidistant between the focus and the directrix, therefore, we split the distance between 47 and 48 to find that y coordinate of the vertex 47.5. We know that the x coordinate is the same as the x coordinate of the focus, 52. Therefore, the vertex is
Also, we know that
From 47.5 to 48 is a positive
Substitute this information into the general form: