SOLUTION: find the equation of the circle satisfying the given conditions and sketch its graph: center @ (3,4) and touching the line x=6

Algebra ->  Circles -> SOLUTION: find the equation of the circle satisfying the given conditions and sketch its graph: center @ (3,4) and touching the line x=6      Log On


   

Question 535695: find the equation of the circle satisfying the given conditions and sketch its graph: center @ (3,4) and touching the line x=6
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Starting with the general form for a circle with center at (h, k) and radius, r.
%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2
The center is given as (3, 4) so substitute h = 3 and k = 4.
%28x-3%29%5E2%2B%28y-4%29%5E2+=+r%5E2
To find the radius r, the distance from the center to the circumference, you know that the circumference touches the line x = 6, so the radius would be the distance from the center (x = 3) to the line (x = 6) which gives you a radius of 6-3 = 3. Now you can complete the equation:
%28x-3%29%5E2%2B%28y-4%29%5E2+=+3%5E2 or
highlight%28%28x-3%29%5E2%2B%28y-4%29%5E2+=+9%29
The graph: