## Conic Sections

##### Created by:

kittykittykitty  on March 12, 2012

##### Description:

Conic sections Ellipses and Parabolas

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# Conic Sections

 (x-h)²=4p(y-k) OPENS:up or down
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#### Definitions

(x-h)²=4p(y-k)
OPENS:
up or down
(x-h)²=4p(y-k)
FOCUS:
(h,k+p)
(x-h)²=4p(y-k)
DIRECTRIX:
y=k-p
(x-h)²=4p(y-k)
AXIS:
x=h
(x-h)²=4p(y-k)
FOCAL LENGTH:
p
(x-h)²=4p(y-k)
FOCAL WIDTH:
|4p|
(y-k)²=4p(x-h)
OPENS:
left or right
(y-k)²=4p(x-h)
FOCUS:
(h+p,k)
(y-k)²=4p(x-h)
DIRECTRIX:
x=h-p
(y-k)²=4p(x-h)
AXIS:
y=k
(y-k)²=4p(x-h)
FOCAL LENGTH:
p
(y-k)²=4p(x-h)
FOCAL WIDTH:
|4p|
x²=4py
OPENS:
up or down
x²=4py
FOCUS:
(0,p)
x²=4py
DIRECTRIX:
y=-p
x²=4py
AXIS:
y-axis
x²=4py
FOCAL LENGTH:
p
x²=4py
FOCAL WIDTH
|4p|
y²=4px
OPENS:
left or right
y²=4px
FOCUS:
(p,0)
y²=4px
DIRECTRIX:
x=-p
y²=4px
AXIS:
x-axis
y²=4px
FOCAL LENGTH:
p
y²=4px
FOCAL WIDTH:
|4p|
(x²/a²)+(y²/b²)=1
FOCAL AXIS:
x-axis
(x²/a²)+(y²/b²)=1
FOCI:
(±c,0)
(x²/a²)+(y²/b²)=1
VERTICES:
(±a,0)
(x²/a²)+(y²/b²)=1
SEMIMAJOR AXIS:
a
(x²/a²)+(y²/b²)=1
SEMIMINOR AXIS:
b
(x²/a²)+(y²/b²)=1
PYTHAGOREAN RELATION:
a²=b²+c²
(y²/a²)+(x²/b²)=1
FOCAL AXIS:
y-axis
(y²/a²)+(x²/b²)=1
FOCI:
(0,±c)
(y²/a²)+(x²/b²)=1
VERTICES:
(0,±a)
(y²/a²)+(x²/b²)=1
SEMIMAJOR AXIS:
a
(y²/a²)+(x²/b²)=1
SEMIMINOR AXIS:
b
(y²/a²)+(x²/b²)=1
PYTHAGOREAN RELATION:
a²=b²+c²
(x-h)²/a² + (y-k)²/b²=1
FOCAL AXIS:
y=k
(x-h)²/a² + (y-k)²/b²=1
FOCI:
(h±c,k)
(x-h)²/a² + (y-k)²/b²=1
VERTICES:
(h±a,k)
(x-h)²/a² + (y-k)²/b²=1
SEMIMAJOR AXIS:
a
(x-h)²/a² + (y-k)²/b²=1
SEMIMINOR AXIS:
b
(x-h)²/a² + (y-k)²/b²=1
PYTHAGOREAN RELATION:
a²=b²+c²
(y-k)²/a² + (x-h)²/b²=1
FOCAL AXIS:
x=h
(y-k)²/a² + (x-h)²/b²=1
FOCI:
(h,k±c)
(y-k)²/a² + (x-h)²/b²=1
VERTICES:
(h,k±a)
(y-k)²/a² + (x-h)²/b²=1
SEMIMAJOR AXIS:
a
(y-k)²/a² + (x-h)²/b²=1
SEMIMINOR AXIS:
b
(y-k)²/a² + (x-h)²/b²=1
PYTHAGOREAN RELATION:
a²=b²+c²
ECCENTRICITY
ELLIPSE:
c/a

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