Completing The Square Examples And Worksheet Page 2
ADVERTISEMENT
1
25. In this example, we take the equation of a circle and convert it to standard form so we can
see what the center and radius of the circle are.
Consider the equation
2
2
+ y
6x + 14y
104 = 0
x
We rewrite it as
2
2
6x + y
+ 14y = 104
x
and complete the square on the x and y terms independently:
2
2
(x
3)
9 + (y + 7)
49 = 104
Moving the constants all to the right side results in the equation
2
2
(x
3)
+ (y + 7)
= 162
This shows that our equation is the equation of the circle with center (3, 7) and radius
√
162.
Exercises
The following equations can be verified in two ways: by completing the square on the left, or
expanding on the right. I recommend that you do both for all of them.
2
2
1. x
10x + 32 = (x
5)
+ 7.
2
2
2. 3x
12x + 1 = 3(x
2)
11.
2
8
25
1
7
2
3. 4x
x +
= 4 x
+
3
9
3
3
2
2
4.
2x
4 =
(x + 1)
3.
x
2
20
356
2
2
2
2
5.
+
=
(x
5)
x
x
.
3
3
21
3
7
2
2
5x
110x
533 =
5(x + 11)
+ 72.
6.
Verify the following statements:
2
2
+ y
6x
8y = 375 has center (3, 4) and radius 20.
1. The circle x
1
59
2
2
1
1
2. The circle x
+ y
+
= 0 has center (
) and radius 2.
x
y
,
4
2
2
16
2
2
123
5
+ 2x + y
+ 12y +
= 0 has center ( 1, 6) and radius
3. The circle x
.
4
2
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education