Step-by-step explanation:
Given Vertex (5,4) and focus (8,4)
It can be easily noticed that focus and vertex lie on the same horizontal line y = 4
Obviously, the axis of symmetry is a horizontal line ( a line perpendicular to y-axis). Also, the focus lies to the right of the vertex so the parabola will open up rightward.
(y−k)^2=4a(x−h)
a=8-5=3 as y coordinates are the same.
Since the focus lies to the left of vertex, a = 3
(y−4)^2=4⋅3⋅(x−5)
(y−4)^2=12(x−5)
is the equation of the parabola.
