Hey guys I'm stuck in this question please help.
1.consider a point M (x; y) of the plan. Recall the formula for obtaining the distance CM.
2.show that CM= R if and only if (x-xc)2 (y-yc)2 =R2
3.to deduce that the circle of center C and radius R is the set of points M (x; y) whose coordinates are
of the equation (x-xc)2+(y-yc)2=R2
Thank you for your help.!
+6250 I don't know what you mean by "the plan" but what the problem seems to be getting after
is that as all points on a circle are equidistant from the center we have the following equation
\(\forall (x,y) \ni (x,y) \text{ is on a circle with radius }R \text{ and center }(x_c, y_c)\\ d = \sqrt{(x-x_c)^2 + (y-y_c)^2} = R\\ \text{and squaring both sides we get}\\ (x-x_c)^2 + (y-y_c)^2 =R^2\)
