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?

Answer 1

let me try hold on and btw cute pic

Answer 2

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

Answer 3

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

Answer 4

Because an intersection occurs when a point meets both equations.

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

4 points