Hyperbole

Formula §

$\frac{(x-h{)}^2}{a^2}-\frac{(y-k{)}^2}{b^2}=1$ (horizontal hyperbole)

$\frac{(y-k{)}^2}{a^2}-\frac{(x-h{)}^2}{b^2}=1$ (vertical hyperbole)

Reminder: go opposite way of the values in the brackets

c${}^2$ = a${}^2$ + b${}^2$ c represents the focus a represents the vertex (up / down a or left right a depending on which type of hyperbola)

Horizontal Hyperbole §

asymptote: $\frac{b}{a}$ & -$\frac{b}{a}$ asymptote: y - k = $\pm$ $\frac{b}{a}$(x-h) e (eccentricity) = $\frac{c}{a}$ e > 1

the vertex is a units left a units right from origin

Vertical Hyperbole §

asymptote: y - k = $\pm$ $\frac{a}{b}$ (x-h) e (eccentricity) = $\frac{c}{a}$ e > 1

the vertex is a units up and a units down from origin focus is c units up and c units down b value is to the right and left and if you connect all the points it creates a box