Finding the center and radius of circles given an equation

[Jim4592]

Homework Statement

Find the center and the radius of the circle with the given equation.

Homework Equations

x²+y²+4y-117=0

The Attempt at a Solution

I first got it in standard form by completing the square:

x²+(y+2)²=121

but i don't know how to get the center and radius of it? I'm pretty sure its given in that form of the equation, right? but I'm not sure which numbers are the ordered pair.

 

[symbolipoint]

Homework Statement

Find the center and the radius of the circle with the given equation.

Homework Equations

x²+y²+4y-117=0

The Attempt at a Solution

I first got it in standard form by completing the square:

x²+(y+2)²=121

but i don't know how to get the center and radius of it? I'm pretty sure its given in that form of the equation, right? but I'm not sure which numbers are the ordered pair.

Your basic standard form for a circle equation is (x-h)²+(y-k)²=r². That form let's you directly read how the center has been translated and also shows the radius.

 

[Georgepowell]

The general equation for a circle is:

(x + a)² + (y + b)² = r²

where (-a,-b) is the centre of the circle and r is the radius.

That should complete your problem, as you have already put it mostly into the right form

 

[Jim4592]

so the center of my circle is (0,-2) and would that make the radius 11, the square root of 121??

 

[tiny-tim]

so the center of my circle is (0,-2) and would that make the radius 11, the square root of 121??

(hmm … everyone else seems to have gone out, so …)

Yup! ​