Circles Worksheet - Honors Pre-calculus

Honors Pre-Calculus
Name ________________________
Circles
Circle: Set of all points in a plane which are the same distance (radius) from a fixed point (center).
Standard form for the equation of a circle:
+
=
2
2
2
(
x
h
)
(
y
k
)
r
circle with center (h, k) and radius r.
General form for the equation of a circle:
+
+
+
+
=
2
2
ax
bx
cy
dy
e
0
We use the Completing the Square method to convert equations from general form to standard form.
Ex1:
2
−12x + 3y
2
+ 30y + 75 = 0
3x
2
−12x + 3y
2
+ 30y = −75
3x
(DIVIDE both sides by 3)
2
− 4 x + y
2
+ 10y = −25
x
2
− 4 x + __ ) + (y
2
+ 10y + __ ) = −25 + __ + __
(x
2
− 4 x + 4) + (y
2
+ 10y + 25) = −25 + 4 + 25
(x
(x − 2)
2
+ (y + 5)
2
= 4
This circle is centered on (2, -5) and the radius = 2
Complete the square to rewrite each equation in to standard form for a circle. Graph each circle.
+
+
+
=
+
=
2
2
2
2
1.
x
y
8
x
16
y
31
0
2.
5
x
10
x
5
y
30
y
75
0
+
+
=
+
+
+
=
2
2
2
2
3.
4
x
4
y
16
y
15
0
4.
2
x
2
y
24
x
36
y
162
0
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