## How to Determine which circle has the larger radius by inspection?

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
mathpatient
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### How to Determine which circle has the larger radius by inspection?

A problem is given with two equations for a circle and I am asked to determine which has the larger radius.

I know how to solve the problem by calculation and answered correctly. But I want to know is there a way to distinguish which circle has the larger radius at first glance without solving extensively?

Here are the two equations of a circle:

x^2 - 16x + y^2 - 8y - 1 = 0

x^2 - 4x + y^2 + 4y - 1 = 0

maggiemagnet
Posts: 358
Joined: Mon Dec 08, 2008 12:32 am
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### Re: How to Determine which circle has the larger radius by inspection?

A problem is given with two equations for a circle and I am asked to determine which has the larger radius.

I know how to solve the problem by calculation and answered correctly. But I want to know is there a way to distinguish which circle has the larger radius at first glance without solving extensively?

Here are the two equations of a circle:

x^2 - 16x + y^2 - 8y - 1 = 0

x^2 - 4x + y^2 + 4y - 1 = 0
I guess you should think about which equation will make you add more to the other side, because the adding is what gives you the radius. For the x's in the first equation you would add 64 and for the y's you would add 16. For the second equation you would add 4 and 4. So the first one must have a bigger radius.