SOLUTION: Please help me with this problem! The path swum by the captain of a synchronized swimming team is modeled by the equation {{{(x-3)^2+(y-2)^2=25}}}. One of her team mates swims in a

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Please help me with this problem! The path swum by the captain of a synchronized swimming team is modeled by the equation {{{(x-3)^2+(y-2)^2=25}}}. One of her team mates swims in a      Log On


   

Question 932634: Please help me with this problem! The path swum by the captain of a synchronized swimming team is modeled by the equation %28x-3%29%5E2%2B%28y-2%29%5E2=25. One of her team mates swims in a path modeled by the equation y%2B%281%2F2%29x%5E2%2Bx=1%2F2. At what point are the two swimmers in danger of colliding?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This is mostly many algebra steps, relying on substitution. Best start is to solve the second equation for y in terms of x, and substitute this into the first equation. Solve for the value of x, first. This should be a long process, but not too complicated.

y=1%2F2-x%5E2%2F2-x
;
%28x-3%29%5E2%2By%5E2-4y%2B4=25, and do the substitution. You might do the squaring of y separately and then include this for y%5E2 in the equation...