The hyperbola has two equations:[br]Horizontal: [math]\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1[/math][br]or [br]Vertical: [math]\frac{\left(y-k\right)^2}{b^2}-\frac{\left(x-h\right)^2}{a^2}=1[/math][br][br]If the hyperbola is horizontal, the transverse axis (the distance from the vertices) is 2a.[br]If the hyperbola is vertical, the transverse axis is 2b.[br][br]The Vertices will be:[br]Horizontal: [math]\left(h+a,k\right)\left(h-a,k\right)[/math][br]Vertical:[math]\left(h,k+b\right)\left(h,k-b\right)[/math][br][br]The The Foci Equation: [br][math]c^2=a^2+b^2[/math][br]Foci: [br]Horizontal: [math]\left(h+c,k\right)\left(h-c,k\right)[/math][br]Vertical: [math]\left(h,k+c\right)\left(h,k-c\right)[/math]