
Conic section(Basic)
Presentation
•
Mathematics
•
10th - 12th Grade
•
Easy
Wren :3
Used 2+ times
FREE Resource
11 Slides • 30 Questions
1
Analytic geometry
By Wren
2
Standard form of equations
Slope intercept form:
y = mx+b
Standard form:
y-mx-b = 0
mx+b-y = 0
This is some hard algebra :P
3
Distance between point and line
Midpoint = ((x1+x2)/2, (y1+y2)/2)
Distance x = x2-x1
Distance y = y2-y1
Distance :
Distance between two points
Distances and midpoints
What is this shit?
4
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7
Multiple Choice
Midpoint of (5,2) and (9,2)
(7,2)
(3,2)
(2,7)
(2,3)
8
Multiple Choice
Midpoint of (-3,3) and (6,9)
(-1.5,-6)
(1.5,6)
(6,1.5)
(-6,-1.5)
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10
Conic section
By Wren
11
Formula
Radius = r
Center = (h, k)
Tangent(เส้นตัดวงกลม) = Linear functions
Structures
Circles
Easiest of the bunch, math teacher makes it look hard.
12
Multiple Choice
Which equation is the standard equation of a circle?
x2+y=9
(x−1)2+x2=4
x2+(y−1)2=1
(x−1)2−(y−1)2=16
13
Multiple Choice
What is the equation of this circle?
(x−1)2+(y−1)2=1
(x+1)2+y2=4
x2+y2=16
(x+3)2+y2=25
14
Multiple Choice
Circle with center at (0,0) and radius of 7
(x+1)2+(y−2)2=36
(x−2)2+(y+1)2=25
x2+y2=6
x2+y2=49
15
Multiple Choice
Circle with center at (3,5) and radius of 4
(x−3)2−(y−5)2=16
(x+3)2+(y+5)2=16
(x+3)2−(y+5)2=16
(x−3)2+(x−5)2=16
16
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Tangent line: ax+by+c = 0
Center = (h1,k1)
Radius:
Radius formula from tangent:
Point on circle(จุดบนวงกลม) = (h2,k2)
Center = (h2,k1)
Radius:
Radius formula from points on circle:
Radius and Tangent line
Circle on crack I guess :P
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21
Multiple Choice
A circle with a center at (6,9) with a point on the circle at (1,-3)
(x−9)2+(y−6)2=144
(x−6)2+(y−9)2=169
(x−9)2+(y−6)2=169
(x−6)2+(y−9)2=144
22
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23
Multiple Choice
A circle with a center at (1,-1) and a tangent line function of 9x+12y+18=0. Which is the equation of this circle?
(x−1)2+(y+1)2=9
(x+1)2+(y−1)2=1
(x−1)2+(y+1)2=1
(x+1)2+(y−1)2=9
24
Formulae:
Major axis(แกนเอก) = a
Minor axis(แกนโท) = b
Center = (h,k)
Focus length = c
Structures:
Ellipses
Circle with extra steps, significantly harder but still understandable.
25
a is on the y-axis
b is on the x-axis
Vertical:
a is on the x-axis
b is on the y-axis
Horizontal:
Direction of ellipses
Two!? I thought one was already bad enough!
26
Multiple Choice
Which is the standard equation for an ellipse?
a2(x+h)2+b2(y+k)2=1
a2(x−h)2+b2(y−k)2=r2
a2(x−h)2−b2(y−k)2=1
a2(x−h)2+b2(y−k)2=1
27
Multiple Choice
36x2+16y2=1
Which direction will the ellipse stretch in?
Horizontally
(แนวนอน)
Vertically
(แนวตั้ง)
28
Multiple Choice
64x2+100y2=1
Which direction will the ellipse stretch in?
Horizontally
(แนวนอน)
Vertically
(แนวตั้ง)
29
Multiple Choice
36(x−2)2+169(y+9)2=1
Which direction will the ellipse stretch in?
Horizontally
(แนวนอน)
Vertically
(แนวตั้ง)
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Focus point is always on the a-axis
c = focus length
a = major axis(แกนเอก)
b = minor axis(แกนโท)
Focus length formula:
Focus point
I thought it was only center and radius and we have this ;-;
33
Multiple Choice
9(x+2)2+4(y−1)2=1
Which axis is the focus length on?
x-axis
y-axis
34
Multiple Choice
25(x+2)2+49(y−1)2=1
Which axis is the focus length on?
x-axis
y-axis
35
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37
Eccentricity formula:
Latus rectum formula:
Latus rectum and Eccentricity
If I were to choose between this and shitting my pants I wouldn't need a toilet.
a = major axis(แกนเอก)
b = minor axis(แกนโท)
a = major axis(แกนเอก)
c = focus length
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End of
Basic Conic section
Analytic geometry
By Wren
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