SOLUTION: Find the equation of the parabola satisfying the given conditions The focus lies on the y-axis, and the parabola passes through the point (7,-10)

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Question 1004791: Find the equation of the parabola satisfying the given conditions
The focus lies on the y-axis, and the parabola passes through the point (7,-10)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This is no specific parabola and therefore the question is open-ended.
You can choose to have axis of symmetry being the y-axis, or being horizontal. You can still accept the specification of the parabola passing through point (7,-10).

Just for making a choice, let the focus be a specific point, (0,3).
If you choose directrix (-6,y), then the vertex would be at (-3,3).
Put the facts into standard form, as x=a%28y-%28-3%29%29%5E2%2B3, and this simply requires you know how to work with standard form equation for parabola.
Simplify just enough...
x=a%28y%2B3%29%5E2%2B3

Now you know the parabola must contain (7,-10). Use this to find a=what.
a%28y%2B3%29%5E2=x-3
a=%28x-3%29%2F%28y%2B3%29%5E2
substitute the coordinates
a=%287-3%29%2F%28-10%2B3%29%5E2
a=4%2F%28-7%29%5E2
a=4%2F49

Put the whole equation together to finish:
highlight%28x=%284%2F49%29%28y%2B3%29%5E2%2B3%29
Just one possible example and certainly not the only possible result for the question.