Elements and asymptotes

From the canonical equation one reads off all the characteristic elements of the hyperbola: foci, vertices, eccentricity and above all the asymptotes, the two lines that the branches of the curve approach indefinitely. The proof of the asymptotes shows why, for large $|x|$, the hyperbola blends with the lines $y=\pm\frac{b}{a}x$.

• Foci, vertices, asymptotes and eccentricity
• Proof of the asymptotes