Given a point ( x 0 </msub> , y 0 </msub> ) and a radi

watch5826c 2022-06-24 Answered
Given a point ( x 0 , y 0 ) and a radius r, how do you find the set of all circles that have that radius that pass through the point?
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Answers (1)

lorienoldf7
Answered 2022-06-25 Author has 19 answers
Step 1
We are interested in circles in the x , y plane, therefore they will have Cartesian equation:
( x x C ) 2 + ( y y C ) 2 = r 2
where their radius r > 0 is fixed, so it remains to understand how to determine the centers.
In particular, given that we want the circles in question all to pass through ( x P , y P ) and at the same time we have radius r > 0 , it's evident that ( x C , y C ) must belong to the circle with center ( x P , y P ) and radius r > 0 , that is:
{ x C = x P + r cos ( u ) y C = y P + r sin ( u ) with u [ 0 , 2 π ) .
In this way, we have determined the Cartesian equation of the sheaf of circles obtainable according to the chosen value of u [ 0 , 2 π )

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