Ellipse/Foci/Quadratic equation/Principal axis/Exercise

Let $Q_1,Q_2\in {ℝ}^2$ be two points, $c>0$, and set

$E=\{P\in {ℝ}^2\mid d(P,Q_1)+d(P,Q_2)=c\}.$

Show that $E$ is the zero set of a quadratic polynomial in two variables. How does the standard form look like? What are the principal axes?

Create a solution