\((x-a)^2 + (y-b)^2 = r^2\)
is the equation for a circle centered at (a,b) with radius r.
I encountered this in GMAT Club test m09. Do we need to know this? This is not covered in MGMAT and I have yet to see it in any other problem I've tried so far.
The equation of a circle in an xy-plane is supposedly an advanced geometry problem. You might want to remember the underlying concept - the pythagorean theorem. Any point (x,y) will lie on the boundary of the circle if the sum of squares of difference of x and y coordinates with respect to the center (a,b) will give you the hypotenuse r squared. In simpler words, the distance between any point (x,y) from the center (a,b) is r. That must be the standard across any circle based on which this equation was developed. GMAC must be testing this standard, not the equation, remembering the equation though can help save some time.
I am AWESOME and it's gonna be LEGENDARY!!!