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Conic Sections
Conic Section Equations
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Conic Sections
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1
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Conic section polynomial
Ax^2 + By^2 + Cx + Dy + E = 0
2
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if the center is (0,0)
the equation is x^2 + y^2 = r^2
3
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if the center is (h,k)
the equation is (x-h)^2 + (y-k)^2 = r^2.
4
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horizontal ellipse (a,0) and (-a,0), a^2 > b^2
x^2 / a^2 + y^2 / b^2 = 1
5
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vertical ellipse (0,a) and (0,-a), a^2 > b^2
x^2 / b^2 + y^2 / a^2 = 1
6
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horizontal ellipse (h,k), a^2 > b^2
(x-h)^2 / a^2 + (y-k)^2 / b^2 = 1
7
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vertical ellipse (h,k), a^2>b^2
(x-h)^2 / b^2 + (y-k)^2 / a^2 = 1
8
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Hyperbola (opens to the sides)
(x-h)^2 / a2 - (y-k)^2 / b^2 = 1
9
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Hyperbola (opens up and down)
(y-k)^2 / a^2 - (x-h)^2 / b^2 = 1
10
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Parabola
y = Ax^2 + Bx + C
11
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If A < 0
the parabola opens downward and its vertex is the highest point on the parabola
12
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If A > 0
then the parabola opens upward and its vertex is the lowest point on the parabola
13
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ellipse
AB > 0
14
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circle
A = B, A and B not equal to 0
15
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parabola
A = 0 or B = 0, but not both
16
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line
A = 0 and B = 0
17
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hyperbola
AB < 0
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