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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.!

 Jan 2, 2019
edited by Guest  Jan 2, 2019
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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

 

\(\forall (x,y) \ni (x,y) \text{ is on a circle with radius }R \text{ and center }(x_c, y_c)\\ d = \sqrt{(x-x_c)^2 + (y-y_c)^2} = R\\ \text{and squaring both sides we get}\\ (x-x_c)^2 + (y-y_c)^2 =R^2\)

.
 Jan 2, 2019

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