In the xy-plane, the parabola with equation y=x^2-4 intersects the ellipse with equation x^2/16 +y^2/4 =1 in how many points?

Question

In the xy-plane, the parabola with equation y=x^2-4 intersects the ellipse with equation x^2/16  +y^2/4  =1  in how many points?

anonymous · Answer

let me try hold on and btw cute pic

kc_kennylau · Answer

That is the same as asking how many solutions exist in the following system:
$$\left\{\begin{array}{}y=x^2-4\\frac{x^2}{16}+\frac{y^2}4=1\end{array}\right.$$

isaiah.feynman · Answer

@kc_kennylau that MIGHT be another of thinking it but I'm not sure.

kc_kennylau · Answer

Because an intersection occurs when a point meets both equations.

isaiah.feynman · Answer

Yes. Try it and I will lazily look somewhere online to graph it.

anonymous · Answer

this is what i got for y when I try to find where they intersect:

kc_kennylau · Answer

https://www.desmos.com/calculator/4uzanwgwgy

kc_kennylau · Answer

4 points

anonymous · Answer

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