SOLUTION: Points O(0,0) and B(0,3) below lie in the standard (x,y) coordinate plane. The collection of all points such that each is twice as far from B as from O forms a circle. The point (s

Algebra ->  Circles -> SOLUTION: Points O(0,0) and B(0,3) below lie in the standard (x,y) coordinate plane. The collection of all points such that each is twice as far from B as from O forms a circle. The point (s      Log On


   

Question 986443: Points O(0,0) and B(0,3) below lie in the standard (x,y) coordinate plane. The collection of all points such that each is twice as far from B as from O forms a circle. The point (sqrt 3, 0) is 1 point on the circle. What are the coordinates of the center of the circle?
F. (sqrt 3/2, 3/2)
G. (0,3/2)
H. (0, 1)
J. (0,-1)
K. (0,-3)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You are saying Distance between (x,y) and B(0,3) is 2 times distance between (x,y) and O(0,0). You are expecting, according to description, the points (x,y) are a circle.

sqrt%28%28x-0%29%5E2%2B%28y-3%29%5E2%29=2%2Asqrt%28%28x-0%29%5E2%2B%28y-0%29%5E2%29
sqrt%28x%5E2%2B%28y-3%29%5E2%29=2sqrt%28%28x%29%5E2%2B%28y%29%5E2%29
x%5E2%2B%28y-3%29%5E2=4%28x%5E2%2By%5E2%29
x%5E2%2B%28y-3%29%5E2=4x%5E2%2B4y%5E2
x%5E2%2By%5E2-6y%2B9=4x%5E2%2B4y%5E2
-6y%2B9=3x%5E2%2B3y%5E2
-2y%2B3=x%5E2%2By%5E2
x%5E2%2By%5E2%2B2y=3
Want standard form, requiring Completing the Square
x%5E2%2By%5E2%2B2y%2B1=3%2B1
highlight%28x%5E2%2B%28y%2B1%29%5E2=4%29
Circle, centered at (0,-1), and radius is sqrt%284%29=highlight%282%29.