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10.7.2: Key Equations

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    116446
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    Key Equations

    Horizontal ellipse, center at origin x 2 a 2 + y 2 b 2 =1,a>b x 2 a 2 + y 2 b 2 =1,a>b
    Vertical ellipse, center at origin x 2 b 2 + y 2 a 2 =1,a>b x 2 b 2 + y 2 a 2 =1,a>b
    Horizontal ellipse, center (h,k) (h,k) ( xh ) 2 a 2 + ( yk ) 2 b 2 =1,a>b ( xh ) 2 a 2 + ( yk ) 2 b 2 =1,a>b
    Vertical ellipse, center (h,k) (h,k) ( xh ) 2 b 2 + ( yk ) 2 a 2 =1,a>b ( xh ) 2 b 2 + ( yk ) 2 a 2 =1,a>b
    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 ( xh ) 2 a 2 ( yk ) 2 b 2 =1 ( xh ) 2 a 2 ( yk ) 2 b 2 =1
    Hyperbola, center at (h,k), (h,k), transverse axis parallel to y-axis ( yk ) 2 a 2 ( xh ) 2 b 2 =1 ( yk ) 2 a 2 ( xh ) 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 ( yk ) 2 =4p( xh ) ( yk ) 2 =4p( xh )
    Parabola, vertex at (h,k), (h,k), axis of symmetry on y-axis ( xh ) 2 =4p( yk ) ( xh ) 2 =4p( yk )
    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 x= x cosθ y sinθ y= x sinθ+ y cosθ x= x cosθ y sinθ y= x sinθ+ y cosθ
    Angle of rotation θ,where cot( 2θ )= AC B θ,where cot( 2θ )= AC B

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