Thread: center and radius of a circle?

1. center and radius of a circle?

how do you find the center and radius of a circle?

Problem:
Find the center of the circle given in general form (x^2)+(y^2)-10x-2y+50=49

2. Originally Posted by lsnyder
how do you find the center and radius of a circle?

Problem:
Find the center of the circle given in general form (x^2)+(y^2)-10x-2y+50=49
Hint: $\displaystyle x^2+y^2-10x-2y+50=49\implies x^2+y^2-10x-2y+25+1+24=49$

Group the proper terms together, such that you generate perfect squares.

Can you take it from here?

3. Originally Posted by Chris L T521
Hint: $\displaystyle x^2+y^2-10x-2y+50=49\implies x^2+y^2-10x-2y+25+4+21=49$

Group the proper terms together, such that you generate perfect squares.

Can you take it from here?

i don't fully understand, sorry...........

4. Originally Posted by lsnyder
i don't fully understand, sorry...........
I'll show the next step.

You should group the terms as follows : $\displaystyle \left(x^2-10x+25\right)+\left(y^2-2y+1\right)=49-24$

The terms in parenthesis on the LHS of the equation factor as perfect squares. On the right side, you'll have the radius value squared.

Can you continue from here?

EDIT: Please refer to my first post. I fixed an error I found in it.

5. Originally Posted by Chris L T521
I'll show the next step.

You should group the terms as follows : $\displaystyle \left(x^2-10x+25\right)+\left(y^2-2y+1\right)=49-24$

The terms in parenthesis on the LHS of the equation factor as perfect squares. On the right side, you'll have the radius value squared.

Can you continue from here?

EDIT: Please refer to my first post. I fixed an error I found in it.

i understand now, thank you very much!