SOLUTION: Write the equation of a circle with a center at (0, 0) and a radius of 5. Write the equation of a circle with a center of (0, 0) and a diameter of 20. Write the equation of a

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write the equation of a circle with a center at (0, 0) and a radius of 5. Write the equation of a circle with a center of (0, 0) and a diameter of 20. Write the equation of a      Log On


   

Question 892696: Write the equation of a circle with a center at (0, 0) and a radius of 5.
Write the equation of a circle with a center of (0, 0) and a diameter of 20.
Write the equation of a circle with a center at (1, 2) and a diameter of 15.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Standard equation for a circle centered at a point (h,k) is highlight_green%28%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2%29

Note that diameter d=2r.

The first circle centered at the origin is highlight%28x%5E2%2By%5E2=5%5E2%29.

Your next two circles work this way.
The diameter of 20 means that r=10, so this circle, centered at origin is highlight%28x%5E2%2By%5E2=100%29.

The last circle of diamter 15 has r=7%261%2F2, and based on its given center,
highlight%28%28x-1%29%5E2%2B%28y-2%29%5E2=%2815%2F2%29%5E2%29
or
highlight%28%28x-1%29%5E2%2B%28y-2%29%5E2=225%2F4%29