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| Equation of a Circle (Standard Form) |
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Definition
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Definition
| Locus(set of pints that satisfy a given condition) of all points in a plane at a given distance from a fixed center. |
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| Center term and Point term |
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Definition
| Center = (h,k). Point = (x,y) |
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| Steps on Graphing a Circle |
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Definition
1)Plot the center
2)Plot the length of the radius
3)Connect |
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Definition
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Definition
| e locus of points that are the same distance from a given point and a given line. |
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| Horizontal Parabola (Standard Form) |
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Definition
(y-k)²=4p(x-h)
+4p=opens RIGHT-focus(h+p,k)-Directrix(x=h-p)-Axis(y-k)
-4p=opens LEFT-focus(h-p,k)-directrix(x=h-p)-axis(y=k) |
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| Vertical Parabola (Standard Form) |
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Definition
(x-h)²=4p(y-k)
+4p=opens UP-focus(h,k+p)-directrix(y=k-p)-axis(x=h)
-4p=opens DOWN-focus(h,k-p)-directrix(y=k+p)-axis(x=h) |
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| Horizontal Parabola General Form |
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Definition
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| Vertical Parabola General Form |
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Definition
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| How do you write an equation of a parabola(on any conic)? |
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Definition
1)Draw a sketch
2)Find which way it faces
3)Use the correct equation
4)Find h,k, and p (any missing variables) |
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Definition
| Locus of points where the SUM of the distances from two given points is constant |
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Definition
Major-Longer end of ellipse (foci ALWAYS on MAJOR axis)
Minor-shorter end of ellipse |
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| What do a, b, and c represent in an ellipse? |
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Definition
a = length of semi-major axis
b = length if semi-minor axis
c = distance from CENTER to FOCUS
Connection: c²+b²=a² |
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| Hamburger Ellipse equation? |
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Definition
(x-h)²/a²+(y-k)²/b²=1
*a always comes from the larger denom!
Foci:(h plus minus c,k)
Vertices:(h plus minus a, k) |
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| Hot Dog Ellipse equation? |
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Definition
(y-k)²/a²+(x-h)²/b²=1
Foci:(h,k plus minus c)
Vertices:(h, k plus minus a) |
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Definition
| Locus of all points where the absolute value of the DIFFERENCES of the distance from two points is constant. |
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Definition
| LINES that APPROACH a HYPERBOLA eventually |
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Definition
| Line of symmetry thru FOCI |
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Definition
| Line of symmetry thru CENTER |
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| a,b, and c in hyperbolas? |
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Definition
a=distance from one vertex to center
b=along with a, it cretes the slope of the asymptotes
c-distance from one foci to the center
a²+b²=c² |
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Definition
(x-h)²/a²-(y-k)²/b²=1
Vertices:(h plus minus a,k)
Foci:(h plus minus c,k)
Asymptotes: y-k=plus minus b/a(x-h) |
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Definition
(y-k)²/a²-(x-h)²/b²=1
Vertices:(h,k plus minus a)
Foci:(h,k plus minus c)
Asymptotes: y-k=plus minus a/b(x-h) |
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| How do you graph a hyperbola? |
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Definition
1) Graph center (h,k)
2) Graph Vertices
3) Count b from the center
4) Draw a dashed box a distance of a and b from the center
5) Draw the asymptotes
6) Graph the hyperbola |
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Definition
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| Variation of General Form of Conic Equations? |
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Definition
Circle - A=C
Parabola - Either A or C is 0
Ellipse - A and C have the same sign, A is not equal to C
Hyperbola - A and C have opposite signs |
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Definition
Ratio of the distance between a point on the graph to a fixed point and a point on the graph to a fixed line.
e = Distance of graph to focus/Distance of graph to directrix
e=c/a |
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Definition
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| Line + Conic system has what # solutions? |
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Definition
| Maybe 0, 1, or 2 solutions |
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| Two Conic System can have up to how many solutions? |
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Definition
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