Geometry Honors: Conic Sections (Kremer)

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Vertical parabola with axis at the origin

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1

Vertical parabola with axis at the origin

y=1/4p(x²)


F(0,p)


d:y=-p

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2

Horizontal parabola with axis at the origin

x=1/p(y²)


F(p,0)


d:x=-p

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3

Vertical parabola

y=1/4p(x-h)²+k


F(h, k+p)


d: y=k-p

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4

Horizontal parabola

y=1/4p(x-k)²+h


F(h+p, k)


d: x=h-p

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5

Circle with center at the origin

x²+y²=r²

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6

Circle

(x-h)²+(y-k)²=r²

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7

Vertical ellipse

((x-h)²)/a²)+(y-k)²/a²)=1


V(h, k±a)


Cov(h±b, k)


F(h, k±c) c²=a²-b²


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8

Horizontal ellipse

((x-h)²/a²)+((y-k)²/b²)=1


V(h±a, k)


Cov(h, k±b)


F(h±c, k) c²=a²-b²

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9

Vertical hyperbola

((y-k)²/a²)+((x-h)²/b²=1


V(h, k±a)


F(h, k±c) c=a²+b²


Asymptote: y=±a/b(x-h)+k

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10

Horizontal hyperbola

((x-h)²/a²)+((y-k)²/b²)


V(h±a,k)

F(h±c,k) c=a²=b²


Asymptote: y=±b/a(x-h)+k

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