conics

# conics - x-axis x h 2 b 2 y k 2 a 2 = 1 major axis is...

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Summary of formulas from chapter 9: __________________________________________________________________ Parabola with vertex V = (h,k) : a = distance(V,focus) = distance (V, directrix) A parabola opens toward the focus and away from the directrix. (y-k) 2 =4a(x-h) opens right ; (x-h) 2 =4a(y-k) opens up (y-k) 2 = - 4a(x-h) opens left ; (x-h) 2 = - 4a(y-k) opens down _______________________________________ Ellipse with center (h,k) : a > b > 0 and a > c > 0 with c 2 = a 2 - b 2 a= distance (center,either vertex),c=distance(center,either foci) The center, foci and vertices all lie on the major axis . x ! h ( ) 2 a 2 + y ! k ( ) 2 b 2 = 1 major axis is parallel to the
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Unformatted text preview: x-axis x ! h ( ) 2 b 2 + y ! k ( ) 2 a 2 = 1 major axis is parallel to the y-axis ____________________________________________________ Hyperbola with center (h,k) : c > a > 0 and c > b > 0 with c 2 = a 2 + b 2 a= distance (center,either vertex),c=distance(center,either foci) The center, vertices and foci all lie on the transverse Equation of hyperbola : Transverse axis : Asymptotes : x ! h ( ) 2 a 2 ! y ! k ( ) 2 b 2 = 1 parallel to x-axis ; y ! k = ± b a ( x ! h ) y ! k ( ) 2 a 2 ! x ! h ( ) 2 b 2 = 1 parallel to y-axis ; y ! k = ± a b ( x ! h )...
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