Question

The equation for a circle is x^2 - 8x + y^2 -8 =0. what is the equation of the circle in standard form?

Answer 1

You have to complete the square on this to get it into standard form of a circle.  Move the 8 over to the other side because that's part of the radius.  Group together the x terms, take half the linear term which is 8, square it and add it in to both sides.  Half of 8 is 4, 4 squared is 16, so add in 16 to both sides.  I'll show you in a sec.  You don't need to do anything to the y squared term.  This just means that the center of the circle does not move up or down, only side to side, right or left.  Here's your completing the square before we simplify it down to its perfect square binomial. $( x^{2} -8x+16)+ y^{2} =8+16$.  Now break down the parenthesis into the perfect square binomial and do the addition of the right: $(x-4) ^{2} + y^{2}=24$.  This is the standard form of a circle that has a center of (4, 0) and a radius of $\sqrt{24}$