Geometry Honors: Conic Sections (Kremer)

Vertical parabola with axis at the origin

y=1/4p(x²)

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F(0,p)

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d:y=-p

Horizontal parabola with axis at the origin

x=1/p(y²)

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F(p,0)

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d:x=-p

Vertical parabola

y=1/4p(x-h)²+k

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F(h, k+p)

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d: y=k-p

Horizontal parabola

y=1/4p(x-k)²+h

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F(h+p, k)

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d: x=h-p

Circle with center at the origin

x²+y²=r²

Circle

(x-h)²+(y-k)²=r²

Vertical ellipse

((x-h)²)/a²)+(y-k)²/a²)=1

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V(h, k±a)

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Cov(h±b, k)

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F(h, k±c) c²=a²-b²

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Horizontal ellipse

((x-h)²/a²)+((y-k)²/b²)=1

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V(h±a, k)

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Cov(h, k±b)

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F(h±c, k) c²=a²-b²

Vertical hyperbola

((y-k)²/a²)+((x-h)²/b²=1

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V(h, k±a)

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F(h, k±c) c=a²+b²

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Asymptote: y=±a/b(x-h)+k

Horizontal hyperbola

((x-h)²/a²)+((y-k)²/b²)

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V(h±a,k)

F(h±c,k) c=a²=b²

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Asymptote: y=±b/a(x-h)+k