SOLUTION: Find the center and radius of the following circle and sketch the graph. X2^ - 2x + y2^ + 8y - 5 = 0

Algebra ->  Linear-equations -> SOLUTION: Find the center and radius of the following circle and sketch the graph. X2^ - 2x + y2^ + 8y - 5 = 0      Log On


   

Question 1052358: Find the center and radius of the following circle and sketch the graph.
X2^ - 2x + y2^ + 8y - 5 = 0
Found 4 solutions by ewatrrr, josgarithmetic, Boreal, advanced_Learner:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 - 2x + y^2 + 8y - 5 = 0
completing the Square
(x-1)^2 + (y+4)^2 - 1 - 16 - 5 = 0
(x-1)^2 + (y+4)^2 = 22
r = sqrt(22)

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Complete the Square for the x and for the y, if necessary, and put into standard form.

x%5E2-2x%2By%5E2%2B8y=5

x%5E2-2x%2B1%2By%5E2%2B8y%2B16=5%2B1%2B16, and do you know why the plus 1 and the plus 16?

%28x-1%29%5E2%2B%28y%2B4%29%5E2=22

Center (1,-4)
Radius sqrt%2822%29
You want to know how to read those from the standard form equation.



y=-4+- sqrt(22-(x-1)^2)

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x^2-2x+y^2+8y=5, moving the 5 across
complete each square, so x^2-2x+1 and y^2+8y+16
(x-1)^2+(y+4)^2=5+1+16; you have to add 1 and 16 to the other side, because they were suddenly added to the left.
The center is at (1,-4), and the radius is sqrt (22)

Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-2x%2By%5E2%2B8y=5
x%5E2-2x%2B1%2By%5E2%2B8y%2B16=5%2B1%2B16
%28x-1%29%5E2%2B%28y%2B4%29%5E2=5%2B1%2B16
%28x-1%29%5E2%2B%28y%2B4%29%5E2=22
%28x-1%29%5E2%2B%28y%2B4%29%5E2=%2822%29

compare it with
%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2