The Equation
What is the equation of a circle?
(x-h)2+(y-k)2=r2
Center (0,0)
Radius 1
x2+y2=1
Find the radius of a circle with the endpoints of diameter. (graph it!)
(0,0) & (6,0)
Radius = 3
Is the point (6,5) on the circle (x-4)2+(y-5)2=4?
Yes
What letters represent the center of the circle in the equation (x-h)2+(y-k)2=r2?
(h,k)
Center (2,3)
Radius 2
(x-2)2+(y-3)2=4
Find the center of a circle with the endpoints of diameter. (Use the midpoint formula)
(1,4) & (7,8)
(4,6)
How can you tell if a point is on a circle? (What are the steps?)
Put the formula for a circle into Desmos. Then, put in the point and see if it lies on the circle.
What letter represents the radius in the equation
(x-h)2+(y-k)2=r2?
r
Center (-1,3)
Radius 3
(x+1)2+(y-3)2=9
Find the Center of a circle with the endpoints of diameter. (Use the midpoint formula)
(3,12) & (9,100)
(6,56)
What is one point that lies on the circle (x-6)2+(y-1)2=16
(6,5)
(6,-3)
(10,1)
(2,1)
What would happen if the h and the k were negative numbers in the equation?
For example: (x+h)2+(y+k)2=r2 instead of (x-h)2+(y-k)2=r2?
The center would be (-h,-k).
Center (-10,-20)
Radius 10
(x+10)2+(y+20)2=100
Find the radius of the circle with the endpoints of diameter. (graph it!)
(1,5) & (1,9)
2
Does the point (0,0) lie on the circle (x+1)2+(y-0)2=25 ?
No
What is wrong with this equation?
(x-h)2+(y-k)2=r
It should be r2.
Center (4,-15)
Radius 5
(x-4)2+(y+15)2=25
Write the equation for the circle with endpoints (4,0) and (4,-8)
Center (4,-4)
Radius 4
Equation (x-4)2+(x+4)2=16
What is one point that lies on the circle (x+1)2+(y-0)2=25 ?
(4,0)
(-6,0)
(4,-4)
(2,4)
(2,-4)
(-4,-4)