Definition and canonical form

The ellipse is the locus of points whose sum of distances from two foci is constant. From this definition, placing the foci at $F_1(-c;0)$ and $F_2(c;0)$, a double squaring yields the canonical equation $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$, where $b^2=a^2-c^2$. The section closes with the classic gardeners’ construction using two nails and a string.

• Definition of the ellipse
• Construction with nails and string
• Canonical equation
• Proof of the canonical equation