SOLUTION: Hi, I an trying to find the x,y position of an arc center when all I know is the radius arc and the x,y points of the beginning and end. For example where is center of a arc drawn

Algebra ->  Trigonometry-basics -> SOLUTION: Hi, I an trying to find the x,y position of an arc center when all I know is the radius arc and the x,y points of the beginning and end. For example where is center of a arc drawn       Log On


   

Question 964588: Hi, I an trying to find the x,y position of an arc center when all I know is the radius arc and the x,y points of the beginning and end. For example where is center of a arc drawn from 5,1 to -3,-5 with a radius of 16? Thanks
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Distance Formula using 16 for the distance from each point. Your description correlates best to finding the equation of a circle with those two given points and radius 16.

sqrt%28%28x-5%29%5E2%2B%28y-1%29%5E2%29=16 and sqrt%28%28x%2B3%29%5E2%2B%28y%2B5%29%5E2%29=16.

system%28%28x-5%29%5E2%2B%28y-1%29%5E2=256%2C%28x%2B3%29%5E2%2B%28y%2B5%29%5E2=256%29.

Solving the system will give the coordinates of the center. ADDITIONAL: You can expect to find two different solutions. The problem description did not give which side of the segment the center of the circle is located. Solve the system of the two equations. The arc is part of either circle.

NOTE: I did not yet finish solving this.