
Conic section(Basic)
Presentation
•
Mathematics
•
10th - 12th Grade
•
Easy
Wren :3
Used 2+ times
FREE Resource
11 Slides • 30 Questions
1
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
Fill in the Blanks
Distance between (2,0) and (10,0)
**Type only number**
Type answer...
5
Fill in the Blanks
Distance between (-3,0) and (3,0)
**Type only number**
Type answer...
6
Fill in the Blanks
Distance between (1,2) and (6,14)
**Type only number**
Type answer...
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)
9
Fill in the Blanks
Distance between (4,10) and line 3y = 4x+4
**Type only number**
Type answer...
10
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
Fill in the Blanks
(x−4)2+y2=196
What is the radius from this equation?
**Type only number**
Type answer...
17
Fill in the Blanks
x2+(y−12)2=64
What is the radius from this equation?
**Type only number**
Type answer...
18
Fill in the Blanks
(x+2)2+(y−3)2=25
What is the center from this equation?
**Type using this format, (h,k)**
**h and k are coordinates**
Type answer...
19
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
20
Fill in the Blanks
A circle with a center at (-1,-1) with a point on the circle at (2,3). What is the radius?
**Type only number**
Type answer...
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
Fill in the Blanks
A circle with a center at (3,2) wit a tangent line function of 12y = -5x-13. What is the radius?
**Type only number**
Type answer...
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:
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)
30
Fill in the Blanks
49x2+81(y−4)2=1
What is the length of the major axis(แกนเอก)?
**Type only number**
Type answer...
31
Fill in the Blanks
144(x−1)2+121(y+3)2=1
What is the length of the minor axis(แกนโท)?
**Type only number**
Type answer...
32
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
Fill in the Blanks
100(x−1)2+64y2=1
Find the focus length from this equation.
**Type only number**
Type answer...
36
Fill in the Blanks
23(x−6)2+144(y+3)2=1
Find the focus length from this equation.
**Type only number**
Type answer...
37
Eccentricity formula:
Latus rectum formula:
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
38
Fill in the Blanks
16(x+69)2+36(y−420)2=1
Find the length of the latus rectum.
**Type only number**
Type answer...
39
Fill in the Blanks
100x2+64(y−1)2=1
Find the eccentricity from this equation.
**Type only numbe**
Type answer...
40
Fill in the Blanks
300x2+400(y−1)2=1
Find the eccentricity from this equation.
**Type only decimal**
Type answer...
41
By Wren
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