Question

what is the equation of a parabola with the vertex (3,7) and the focus (5,7)?​

Answer 1

Answer:

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Answer 2

Answer:

( y - 7 )² = 4 (2) ( x - 3)²

Step-by-step explanation:

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)²

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 - 3)²

OR

y²+49-14y = 8 ( x²+9-6x )

y²-14y+49 = 8x²-48x+72

8x²-y²-49x-14y+23 =0