What is the locus of a point that moves such that the sum of its distances from two fixed points is constant?

Hint: Start with $\sqrt{x^2+(y-2)^2}+\sqrt{x^2+(y+2)^2}=6$, and then rewrite this as $\sqrt{x^2+(y-2)^2}=6-\sqrt{x^2+(y+2)^2}$.

Then square both sides, isolate the remaining square root, divide by -4, and then square both sides again.

Another way to do this is to first find points $(0,a)$ and $(0,-a)$ on the y-axis which satisfy the given condition, and then find points $(b,0)$ and $(-b,0)$ which also satisfy this condition.

Then you could use the form $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$ for the ellipse, since it has center at the origin and axes which are parallel to the coordinate axes.

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