Chapter 7, Conic Sections - Section 7.2 - Ellipses - 7.2 Exercises - Page 564: 57

Intersection points: $(0,2)$ and $(0,-2)$ $4x^2+y^2=4$ (Red) $4x^2+9y^2=36$ (Green)

$4x^2+y^2=4$ $4x^2=4-y^2$ $4x^2+9y^2=36$ $4-y^2+9y^2=36$ $8y^2=32$ $y^2=\frac{32}{8}=4$ $y=±2$ $4x^2=4-y^2$ $4x^2=4-4$ $4x^2=0$ $x=0$ Intersection points: $(0,2)$ and $(0,-2)$