Center: (h, k) AOS: x = h and y = k Orientation: Horizontal if a >b Vertical if aPowerPoint PPT...
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• Center: (h, k) • AOS: x = h and y = k • Orientation: Horizontal if a >b Vertical if a<b 2 2 2 2 ( ) ( ) 1 x h y k a b • Vertices: endpoints of major axis • Covertices: endpoints of minor axis • Foci: the points c distance from center • Cone cut by a plane at an angle through the sides • Real World: Tunnels Vertical Ellipse Horizontal Ellipse Major axis Minor axis b b b b a a a a
description
Cone cut by a plane at an angle through the sides Real World: Tunnels. Center: (h, k) AOS: x = h and y = k Orientation: Horizontal if a >b Vertical if a
Transcript of Center: (h, k) AOS: x = h and y = k Orientation: Horizontal if a >b Vertical if aPowerPoint PPT...
• Center: (h, k) • AOS: x = h and y = k• Orientation: Horizontal if
a >b Vertical if a<b
2 2
2 2( ) ( ) 1x h y ka b • Vertices:
endpoints of major axis
• Covertices: endpoints of minor axis
• Foci: the points c distance from center
• Cone cut by a plane at an angle through the sides
• Real World:
Tunnels
Vertical Ellipse
Horizontal Ellipse
Major axis
Minor axis
b
b
b
b
aa a a
Steps to graph1)Find center2)Square root a2 and b2 3)Find c4)Plot center5)Count left and right a spaces6)Count up and down b spaces7)Connect those 4 with curve.8)Count c spaces on major axis both directions to find Foci.
Ex 3) Write the equation given the graph
Ex 1) Graph
Ellipse
Steps to write equation1)Find center2)Find a and square it3)Find b and square it4)Substitute into formula.
Center: (5, -2)a = b=c=
Vertices:(1, -2) (9, -2)Covertices:(5, 1) (5, -5)AOS: x=5 and y=-2
Ex 2) Graph2 2( 5) ( 2)
116 9
x y
2 2( 3)1
4 25
x y
16 49 316 9 7
7 2.6
4 2Center: (-3, 0)a = b=c=
Vertices:(-3, 5) (-3, -5)Covertices:(-1, 0) (-5, 0)AOS: x=-3 and y=0 (x-axis)
25 525 4 21
21 4.6
2 2( 1) ( 2)1
9 36
x y
Center: (-1, -2)a = 3b= 6
Change to Conic Form: Complete the Square
• 1 variable squared • 2 variables squared
• Squared variable coefficient >1 • Pre-AP Only
x2 + y2 -2x - 4y – 4 = 0(x2 -2x + ___) + (y2 - 4y + ____) = - 4 + ____ + ____(-2/2)=-1 then (-1)2=1 AND (-4/2)=-2 then (-2)2=4(x2 -2x + 1) + (y2 - 4y + 4) = - 4 + 1 + 4
(x-1)2 + (y-2)2 = 1
9x2 + 4y2 - 54x - 8y – 59 = 09x2 - 54x + 4y2 - 8y = 599(x2 - 6x +__) + 4(y2 - 2y + __) = 59 + 9(__) + 4(__)
(-6/2)2=9 and (-2/2)2=19(x2 - 6x +9) + 4(y2 - 2y + 1) = 59 + 9(9) + 4(1)
9(x – 3)2 + 4(y – 1)2 = 144
y2 + x + 10y + 26 = 0y2 + 10y + ___ = -x – 26 + ___(10/2)=5 then 52 =25y2 + 10y + 25 = -x – 26 + 25(y+5)2 = -x – 1(y+5)2 = -(x +1)
6x2 + 12x - y + 15 = 06x2 + 12x + __ = y – 15 + ___6(x2 + 2x + __) = y – 15 + 6(__)(2/2)=1 then 12=16(x2 + 2x + 1) = y – 15 + 6(1)6(x+1)2 = y – 9
1) GMA (Group, move, add blanks)2) Fill in blanks3) Factor and simplify
2 2( 3) ( 1) 116 36x y 1) GMA (Group, move, add blanks)
2) Factor out GCF and add to blank on other side
3) Fill in blanks4) Factor and simplify
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