12.1 The ellipse  (Page 8/16)

An ellipse is the set of all points in the plane the sum of whose distances from two fixed points, called the foci, is a constant.

This special case would be a circle.

It is symmetric about the x -axis, y -axis, and the origin.

yes; $\frac{x^2}{3^2}+\frac{y^2}{2^2}=1$

yes; $\frac{x^2}{{\left(\frac{1}{2}\right)}^2}+\frac{y^2}{{\left(\frac{1}{3}\right)}^2}=1$

$\frac{x^2}{2^2}+\frac{y^2}{7^2}=1;$ Endpoints of major axis $\left(0,7\right)$ and $\left(0,-7\right).$ Endpoints of minor axis $\left(2,0\right)$ and $\left(-2,0\right).$ Foci at $\left(0,3\sqrt{5}\right),\left(0,-3\sqrt{5}\right).$

$\frac{x^2}{{\left(1\right)}^2}+\frac{y^2}{{\left(\frac{1}{3}\right)}^2}=1;$ Endpoints of major axis $\left(1,0\right)$ and $\left(-1,0\right).$ Endpoints of minor axis $\left(0,\frac{1}{3}\right),\left(0,-\frac{1}{3}\right).$ Foci at $\left(\frac{2\sqrt{2}}{3},0\right),\left(-\frac{2\sqrt{2}}{3},0\right).$