SOLUTION: The equation x^2+y^2-2x-4y-4=0 represents a circle. What are the coordinates for the center of the circle? What is the length of the radius of the circle?

Algebra ->  Circles -> SOLUTION: The equation x^2+y^2-2x-4y-4=0 represents a circle. What are the coordinates for the center of the circle? What is the length of the radius of the circle?       Log On


   

Question 1026719: The equation x^2+y^2-2x-4y-4=0 represents a circle. What are the coordinates for the center of the circle? What is the length of the radius of the circle?
Answer by mathmate(429) About Me  (Show Source):
You can put this solution on YOUR website!

Question:
The equation x^2+y^2-2x-4y-4=0 represents a circle. What are the coordinates for the center of the circle? What is the length of the radius of the circle?

Solution:
The general equation of a circle centred at (a,b) with radius r is written as:
%28x-a%29%5E2%2B%28y-b%29%5E2=r%5E2........ (1)
By completing squares, we have
x%5E2%2By%5E2-2x-4y-4
=x%5E2-2x%2B1-1+%2B+y%5E2-4y%2B4-4+-4
=%28x-1%29%5E2+-1+%2B+%28y-2%29%5E2+-4+-4+
=%28x-1%29%5E2%2B%28y-2%29%5E2-9
=0
Hence the equation of the circle can be rewritten as
(x-1)^2+(y-2)^2=3^3
By comparison with the general equation (1) above, we conclude that the centre of the circle is (a,b)=(1,2) and the radius is 3.