Algebra and Trigonometry

# Key Equations

 Horizontal ellipse, center at origin Vertical ellipse, center at origin Horizontal ellipse, center $(h,k) (h,k)$ Vertical ellipse, center$(h,k) (h,k)$
 Hyperbola, center at origin, transverse axis on x-axis $x 2 a 2 − y 2 b 2 =1 x 2 a 2 − y 2 b 2 =1$ Hyperbola, center at origin, transverse axis on y-axis $y 2 a 2 − x 2 b 2 =1 y 2 a 2 − x 2 b 2 =1$ Hyperbola, center at$(h,k), (h,k),$transverse axis parallel to x-axis $( x−h ) 2 a 2 − ( y−k ) 2 b 2 =1 ( x−h ) 2 a 2 − ( y−k ) 2 b 2 =1$ Hyperbola, center at$(h,k), (h,k),$transverse axis parallel to y-axis $( y−k ) 2 a 2 − ( x−h ) 2 b 2 =1 ( y−k ) 2 a 2 − ( x−h ) 2 b 2 =1$
 Parabola, vertex at origin, axis of symmetry on x-axis $y 2 =4px y 2 =4px$ Parabola, vertex at origin, axis of symmetry on y-axis $x 2 =4py x 2 =4py$ Parabola, vertex at$(h,k), (h,k),$axis of symmetry on x-axis $( y−k ) 2 =4p( x−h ) ( y−k ) 2 =4p( x−h )$ Parabola, vertex at$(h,k), (h,k),$axis of symmetry on y-axis $( x−h ) 2 =4p( y−k ) ( x−h ) 2 =4p( y−k )$
 General Form equation of a conic section $A x 2 +Bxy+C y 2 +Dx+Ey+F=0 A x 2 +Bxy+C y 2 +Dx+Ey+F=0$ Rotation of a conic section Angle of rotation