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)

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) (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 , and this simply requires you know how to work with standard form equation for parabola.
Simplify just enough...

Now you know the parabola must contain (7,-10). Use this to find .

substitute the coordinates

Put the whole equation together to finish:

Just one possible example and certainly not the only possible result for the question.
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