Geometry Honors: Conic Sections (Kremer)

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Geometry & Trigonometry

Conic Sections

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10 Terms

1
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Vertical parabola with axis at the origin

y=1/4p(x²)

F(0,p)

d:y=-p

2
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Horizontal parabola with axis at the origin

x=1/p(y²)

F(p,0)

d:x=-p

3
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Vertical parabola

y=1/4p(x-h)²+k

F(h, k+p)

d: y=k-p

4
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Horizontal parabola

y=1/4p(x-k)²+h

F(h+p, k)

d: x=h-p

5
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Circle with center at the origin

x²+y²=r²

6
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Circle

(x-h)²+(y-k)²=r²

7
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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

8
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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

9
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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

10
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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