
Equation of a Circle
Presentation
•
Mathematics
•
10th Grade
•
Practice Problem
•
Medium
Standards-aligned
Alicia Brunette
Used 2K+ times
FREE Resource
8 Slides • 12 Questions
1
Equation of a Circle
Learning Target: I can write the equation of a circle and graph a circle from it's equation.
2
Multiple Choice
What does the equation of a circle with center at (0,0) look like?
y=x2
y=mx+b
x2+y2=r2
y=a(x−h)2+k
3
Equation of a circle with center at (0,0)
The equation we use for a circle with the center at (0,0) is
the r stands for the radius of the circle.
4
Multiple Choice
5
Multiple Choice
6
Multiple Choice
7
What if the center isn't (0,0)?
Think back to tranformations of parabolas, we used the point (h,k) to talk about our vertex.
We can use the same point to talk about the center of our circle.
8
Equation of a circle
(x−h)2+(y−k)2=r2
Here (h,k) is the center of the circle and r is the raidus.
9
Open Ended
Why has there not been and h and k value in the equations we have looked at so far, like this one?
10
Writing Equations of Circles
We can write equations of circles from their graphs.
Locate the center of the circle. This usually marked with a dot
11
Multiple Choice
What is the center of this circle?
(2, 2)
(2, -2)
(0, 0)
(-2, 2)
12
Writing Equations of Circles
The other piece of information we need is the radius.
You can calculate the radius by counting the number of units from the center to any point on the circle.
13
Multiple Choice
What is the radius of this circle?
2
6
3
5
14
Writing Equations of Circles
Now we can place our values into our equation
(x−(−2))2+(y−(2))2=(3)2
Then simplify
(x+2)2+(y−2)2=9
15
Notice that the coordinates for the center (h,k) have the opposite sign in the equation. Our (h,k) was (-2, 2), but in the final equation it was
(x +2) 2 and (y−2)2
16
Multiple Choice
What is the equation of the circle?
(x+1)2 + (y +1)2 = 3
(x+1)2 + (y -1)2 = 3
(x+1)2 + (y +1)2 = 9
(x-1)2 + (y -1)2 = 9
17
Multiple Choice
(x-4)2+(y+2)2=25
18
Multiple Choice
(x+7)²+(y-2)²=144?
19
Multiple Choice
20
Multiple Choice
(x)2+ (y-6)2=9
Equation of a Circle
Learning Target: I can write the equation of a circle and graph a circle from it's equation.
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