What is the equation of a parabola with the vertex(3,7) and the focus(5,7)
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Given Vertex (3,7) and focus (5,7).
It can be easily noticed that focus and vertex lie on the same horizontal line y = 7.
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 = 5 - 3 = 2 as y coordinates are the same.
Since the focus lies to the left of vertex, a = 2.
(y - 7)^2 = 4⋅2.(x - 5)
(y - 7)^2 = 8(x - 5) is the equation of the parabola.
Step-by-step explanation:
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