SOLUTION: Find the equation of the circle passing through the origin and with the center (3,5) The answer should be written in the form (x-h) squared + (y-h)squared = radius squared

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the equation of the circle passing through the origin and with the center (3,5) The answer should be written in the form (x-h) squared + (y-h)squared = radius squared       Log On


   

Question 581656: Find the equation of the circle passing through the origin and with the center (3,5)

The answer should be written in the form (x-h) squared + (y-h)squared = radius squared
Thanks!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: the origin is the point (0,0)

%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 Start with the general equation of a circle.


%28x-0%29%5E2%2B%28y-0%29%5E2=r%5E2 Plug in h=0 and k=0 (since the center is the point (h,k) ).


%283-0%29%5E2%2B%285-0%29%5E2=r%5E2 Plug in x=3 and y=5 (this is the point that lies on the circle, which is in the form (x,y) ).


%283%29%5E2%2B%285%29%5E2=r%5E2 Combine like terms.


9%2B25=r%5E2 Square each term.


34=r%5E2 Add.


So because h=0, k=0, and r%5E2=34, this means that the equation of the circle with center (0,0) that goes through the point (3,5) is


%28x-0%29%5E2%2B%28y-0%29%5E2=34.


which simplifies to x%5E2%2By%5E2=34.


So the answer is x%5E2%2By%5E2=34