Chapter Closure
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Recall that the graphing form of a circle is (x-h)^2+(y-k)^2=r^2.
Recall that the graphing form of a circle is (x-h)^2+(y-k)^2=r^2.
Recall that the graphing form of a circle is (x-h)^2+(y-k)^2=r^2.
Recall that the graphing form of a circle is (x-h)^2+(y-k)^2=r^2.
Center: (0,3)
Radius: 6
Center: (-1, -2)
Radius: sqrt(8)
Center: (4, -1)
Radius: 4
Center: (0,-10)
Radius: 10
We want to identify the center and the radius of the given circle based on its equation. Let's recall the graphing form of an equation of a circle.
Like in Part A, let's first rewrite the given equation so that it is in graphing form.
Like in Parts A and B, we will first rewrite the given equation so that it is in graphing form. This time we will need to do it by completing the square.
Split into factors
LHS+4^2=RHS+4^2
LHS+1^2=RHS+1^2
Commutative Property of Addition
a^2± 2ab+b^2=(a± b)^2
Calculate power
Add terms
a+b=a-(- b)
Now we see that ( 4, -1) is the center and 4 is the radius of the given circle.
Like in Parts A-C, we will first rewrite the given equation so that it is in graphing form. Again, we will need to complete the square
Split into factors
LHS+10^2=RHS+10^2
a^2+2ab+b^2=(a+b)^2
Identity Property of Addition
a+b=a-(- b)
Now we see that ( 0, - 10) is the center and 10 is the radius of the given circle.