# Equation of a constrained circle

조회 수: 3(최근 30일)
Sven 2013년 5월 18일
I have a circle with known parameters (x,y,r):
x = 37
y = -7
r = 38
I would like to find the parameters of a new circle (x2,y2,r2) that:
1. Passes through the origin [0,0]
2. Passes through the point [x,y+r]
3. Keeps the same x value (ie, x2==x)
Can anyone wrap their head around this one? Basically it's like pinning the max-y point on the first circle, and then growing-shrinking that circle until it crosses the origin.
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Sven 2013년 5월 18일
Thanks Roger. Don't worry, not homework... I was just about to get on a long flight and this was bugging me. With your prompting I got there. I'd gone down that route but used wolfram alpha without taking the time to think about it... it doesn't like variables called x2 (interprets them as 2*x). I got flustered and was in a hurry, hence the question here :)
As a W.A. string: (0-x)^2+(0-b)^2 = c^2, (y+r-b)^2 = c^2, solve for b, c

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### 답변(1개)

Youssef Khmou 2013년 5월 18일
hi try to verify this initiation :
the first circle is defined by :
a=37;b=-7;r=38;
We are looking for new circle based on The three conditions :
1.a2^+b2^=r2^2
2.(a-a2)²+((b+r)-b2)^2=r2^2
3.a2=a;
the solution is ( to be verified ):
a2=a;
b2==((b+r)^2+a^2)/(2*(b+r));
r2=r2=b+r-b2;
....

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