How does x^2 + y^2 = 4x give the equation of a circle?

Question

anonymous · Answer

subtract 4x from both sides, then solve for y.  this should give you the formulas for the upper and lower semicircle

anonymous · Answer

not exactly you'll have to complete the square

anonymous · Answer

well, yeah you can do that do

anonymous · Answer

if you subtract -4x you'll get 0=y^2+x^2-4x... if you complete the square you'll get

$$y^2+x^2-4x+4=4$$

$$=y^2+(x-2)^2=4$$

you can go farther if you'd like but you don't need to divide by 4 and you'll get the 1 by itself which is considered another equation of a circle

anonymous · Answer

$$=\frac{y^2}{4}+\frac{(x-2)^2}{4}$$

anonymous · Answer

=1

kirbykirby · Answer

Is completing the square the only otion it seems?

anonymous · Answer

i believe so or you can do it the way that lagrange said but i think what they call his is Cartesian and it gives two semi circles which complete the circle

kirbykirby · Answer

Oh ok thanks!!