Answer:
[tex]{(x - 5)}^{2} = 4(y - 2)[/tex]
Step-by-step explanation:
A parabola with vertex at (5, 2) and a directrix y = 1 is a vertical parabola that opens up.
The distance from the vertex to the directrix p=2-1=1 units.
The equation is given by:
[tex] {(x - h)}^{2} = 4p(y - k)[/tex]
where (h,k)=(5,2) is the vertex.
We substitute the values to get:
[tex]{(x - 5)}^{2} = 4(1)(y - 2)[/tex]
[tex]{(x - 5)}^{2} = 4(y - 2)[/tex]
Or
[tex]y = \frac{1}{4} ( {x - 5)}^{2} + 2[/tex]
