Circle Equations
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1College Preparatory Program • Saudi Aramco
Circle Equations
Circle Equations
1. “CENTER RADIUS FORM -CRF”
2
2
2
a. Center at Origin:
x
y
r
2
2
2
b. Center (h,k), i.e., Not at Origin:
x
h
y
k
r
2
2
2. “GENERAL FORM-GF”:
ax
ay
bx
cy
d
0
a. Complete the Square
b. Find the Center and Radius
c. Graph if required!
2
3. OTHER FORMULAS:
Area
r
Circumfere
nce
2
r
4. Find the equation of the circle containing the following data:
a. Center (1,-2) with radius 3.
i.
CRF: _______________________________
ii.
GF: _______________________________ _
b. Center (1,-2) thru point (3,4).
i.
CRF: _______________________________
ii.
GF: _______________________________ _
c. With Diameter Endpoints (1,-2) and (-3,2)
i.
CRF: _______________________________
ii.
GF: _______________________________ _
2
2
d. With General Equation:
3
x
3
y
18
x
12
y
12
0
i.
CRF: _______________________________
ii.
GF: _______________________________ _
e. Write Equation of Circle in CRF with Center (2,-1) and graph:
i.
Tangent to x-axis: _______________________________
ii.
Tangent to y-axis: _______________________________
f.
Write Equation of Circle in GF containing P(0,4), Q(2,3),& R(-2,-1).
GF: _______________________________________
g. Find the distance from P(2,-1) to its tangents of the circle
.
2
2
x
y
4
x
2
y
1
0
distance = _________________ units (accurate to 3 decimal places)
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