The point (-3,3) is on a circle with the center (1,3). Write the standard equation of the circle. (HINT : Find the Radius First). Show all work

Question

I was absent today and im struggling with this problem , If some one can help me i would appreciate it :)

Answer 1

Since you know the point with coordinates (-3,3) is on the circle and the center is at (1,3), you can find the radius.  The radius is the distance from the center of the circle to any point on the circle.  Since the two points above have the same y-value (y=3), you can see that the distance between them is 4.  (Quickly graph these points if that doesn't make sense.)

 

The general form for a circle equation is:

 

(x-h)^2 + (y-k)^2 = r^2

 

(h,k) is the center of the circle, so plug in h=1 and k=3.  Using r=4, the equation becomes:

 

(x-1)^2 + (y-3)^2 = 16