Conic Sections

# Conic Sections - Asymptotes Opens 1 2 2 2 2 = − b y a x...

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Conic Sections Standard Forms of the Equation of a Parabola Equation Vertex Focus Directrix Axis of Symmetry Opens py x 4 2 = ) 0 , 0 ( ) , 0 ( p p y = y -axis up or down px y 4 2 = ) 0 , 0 ( ) 0 , ( p p x = x -axis right or left ) ( 4 ) ( 2 k y p h x = ) , ( k h ) , ( p k h + p k y = vertical line up or down ) ( 4 ) ( 2 h x p k y = ) , ( k h ) , ( k p h + p h x = horizontal line right or left

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Standard Forms of the Equation of an Ellipse Equation Center Major Axis Minor Axis Vertices Foci * b a b y a x > = + , 1 2 2 2 2 ) 0 , 0 ( on the x -axis length = 2 a on the y -axis length = 2 b ( ) ( ) 0 , 0 , a a ( ) ( ) 0 , 0 , c c b a a y b x > = + , 1 2 2 2 2 ) 0 , 0 ( on the y -axis length = 2 a on the x -axis length = 2 b ( ) ( ) a a , 0 , 0 ( ) ( ) c c , 0 , 0 b a b k y a h x > = + , 1 ) ( ) ( 2 2 2 2 ) , ( k h parallel to the x -axis length = 2 a parallel to the y -axis length = 2 b ( ) ( ) k a h k a h , , + ( ) ( ) k c h k c h , , + b a a k y b h x > = + , 1 ) ( ) ( 2 2 2 2 ) , ( k h parallel to the y -axis length = 2 a parallel to the x -axis length = 2 b ( ) ( ) a k h a k h + , , ( ) ( ) c k h c k h + , , * To find the coordinates of the foci, use the formula: 2 2 2 b a c = .
Standard Forms of the Equation of a Hyperbola Equation Center Transverse Axis Vertices Foci * Asymptotes Opens
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Unformatted text preview: * Asymptotes Opens 1 2 2 2 2 = − b y a x ) , ( on the x-axis ( ) ( ) , , a a − ( ) ( ) , , c c − x a b y ± = left and right 1 2 2 2 2 = − b x a y ) , ( on the y-axis ( ) ( ) a a − , , ( ) ( ) c c − , , x b a y ± = up and down 1 ) ( ) ( 2 2 2 2 = − − − b k y a h x ) , ( k h parallel to the x-axis ( ) ( ) k a h k a h , , − + ( ) ( ) k c h k c h , , − + ) ( ) ( h x a b k y − ± = − left and right 1 ) ( ) ( 2 2 2 2 = − − − b h x a k y ) , ( k h parallel to the y-axis ( ) ( ) a k h a k h − + , , ( ) ( ) c k h c k h − + , , ) ( ) ( h x b a k y − ± = − up and down * To find the coordinates of the foci, use the formula: 2 2 2 b a c + = ....
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