How do you complete the square when two variable are included?

[prosoccer747]

Show that the equation

x^2+y^2-4x+10y+13=0

represents a circle. Find the center and radius.

This problem is to be turned in at the beginning of class

 

[daveb]

You'll have to show us what you've attempted and where you're stuck. We don't just provide answers, since you don't learn anything that way.

 

[prosoccer747]

I know how to complete the square in a basic x^2+(1/2)x+2=0. If i could just get a hint as to how to deal with the y variable, that would help

 

[Mark44]

Use the same process on the y terms as you are doing on the x terms.

 

[daveb]

Do you know whatthe form of the equation for a circle is?

 

[prosoccer747]

No i do not know the form

 

[Mark44]

Here's your equation:
x² + y² - 4x + 10y + 13=0

Group the x terms together and the y terms together.
x² - 4x + y² + 10y= -13

Complete the square in the x terms and complete the square in the y terms.

One form for the equation of a circle is (x - a)² + (y - b)² = r². This circle's center is at (a, b) and its radius is r. That's the form you're shooting for.

 

[prosoccer747]

Thank you so much for the help.

 

[prosoccer747]

I solved it and came up with (x-2)^2+(y+5)^2=16 meaning the center is at (2,-5) and the radius=4. Is this what you came up with as well?

 

[rock.freak667]

I solved it and came up with (x-2)^2+(y+5)^2=16 meaning the center is at (2,-5) and the radius=4. Is this what you came up with as well?

That should be correct.