Question

Another circle question. Find the center and radius of: x^2 + y^2 + x + y - (1/2)=0

Answer 1

So the 'standard' form of the circle equation is

(x-a)^2 + (y-b)^2 = c^2

where the center is at (a,b) and the circle has radius c.

So to answer your question, you need to manipulate the equation of the question to get it into this 'standard' form.

Answer 2

(Other responders: please let them think it through for a moment)

Answer 3

so since there is no coefficient with x and y do you do (1/2)squared?

Answer 4

you need to 'complete the square'

x^2 + x = (x -a)^2 + something

for what 'a' and 'something'?

Answer 5

x^2 + y^2 + x +y = 1/2
x^2 + y^2 + x + y = 0.5
x^2 + x + y^2 + y = 0.5
2ac = 1
a = 1 -> c = 0.5
x^2 + x + (0.5)^2 - (0.5)^2 + y^2 + y +(0.5)^2 - (0.5)^2 = 0.5
(x+0.5)^2 + (y+0.5)^2 = 1
center : -0.5,-0.5
radius = 1

Answer 6

Ok i got it thank you both for your help