How do you write the equation x^2 + y^2 – x + 2y + 1 = 0 into standard form?

1 Answer
Dec 10, 2015

(x-1/2)^2+(y+1)^2=1/4

Explanation:

Sort the x-terms and y-terms.

color(blue)(x^2-x)+color(red)(y^2+2y)=-1

Now, complete the square for each variable.

color(blue)(x^2-x+1/4)+color(red)(y^2+2y+1)=-1 color(blue)(+1/4) color(red)(+1)

Don't forget to balance both sides of the equation. (If you add something to one side, add it to the other side as well.)

color(blue)((x-1/2)^2)+color(red)((y+1)^2)=1/4

This is in the standard form of a circle

(x-h)^2+(y-k)^2=r^2

Where:
(h,k) is the center and r is the length of the radius.

Thus, this is a circle with a center at (1/2,-1) and a radius of 1/2.

enter image source here

Here's a graph. (Notice the center at (0.5,-1) and a diameter of 1.)