SOLUTION: What is the standard equation of the parabola having the vertex of (7,11) and focus of (16,11)?

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Question 1063730: What is the standard equation of the parabola having the vertex of (7,11) and focus of (16,11)?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You know focus and vertex. The directrix is the line 16-7=9 units away from the vertex, but on the other side of the vertex than the focus. The directrix is the line x=-2.
You also call this the point (-2,y).

Look in your book for the definition of a parabola, and setup this equation:
sqrt%28%28x-%28-2%29%29%5E2%2B%28y-y%29%5E2%29=sqrt%28%28x-16%29%5E2%2B%28y-11%29%5E2%29

Simplify that equation.
sqrt%28%28x%2B2%29%5E2%29=sqrt%28%28x-16%29%5E2%2B%28y-11%29%5E2%29
%28x%2B2%29%5E2=%28x-16%29%5E2%2B%28y-11%29%5E2
x%5E2%2B4x%2B4=x%5E2-32x%2B256%2By%5E2-22y%2B121
4x%2B4=-32x%2B256%2By%5E2-22y%2B121
36x%2B4=y%5E2-22y%2B377
36x=y%5E2-22y%2B373
36x=y%5E2-22y%2B11%5E2%2B373-11%5E2, completing the square because you wanted standard form
36x=%28y-11%29%5E2%2B252

x=%281%2F36%29%28y-11%29%5E2%2B252%2F36

252/36=28/4=14/2=7

highlight%28x=%281%2F36%29%28y-11%29%5E2%2B7%29