SOLUTION: HOW DO I FIND THE EQUATION OF A CIRCLE WHERE THE CENTER IS (-3, 4) AND A POINT ON THE EDGE IS (4, 6).

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: HOW DO I FIND THE EQUATION OF A CIRCLE WHERE THE CENTER IS (-3, 4) AND A POINT ON THE EDGE IS (4, 6).      Log On


   

Question 11418: HOW DO I FIND THE EQUATION OF A CIRCLE WHERE THE CENTER IS (-3, 4) AND A POINT ON THE EDGE IS (4, 6).
Found 2 solutions by Earlsdon, askmemath:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You use the standard form for the equation of a circle with center at (h, k) and radius of r.
%28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2
You know where the center is: (-3, 4) so that h = -3 and k = 4 Plug these into the formula:
%28x-%28-3%29%29%5E2+%2B+%28y-4%29%5E2+=+r%5E2
%28x%2B3%29%5E2+%2B+%28y-4%29%5E2+=+r%5E2 Now you need to find the radius r.
The radius is just the distance form the circle center to a point on the circumference. You have the location of the center (-3, 4) and the location of a point on the circumference (4, 6).
You can use the distance formula to find the length of the radius using these two points:
d+=+sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29
d+=+sqrt%28%284-%28-3%29%29%5E2+%2B+%286-4%29%29%5E2%29
d+=+sqrt%287%5E2+%2B+2%5E2%29
d+=+sqrt%2849+%2B+4%29
d+=+sqrt%2853%29 This is the length of the radius r, but you really want r^2, so you will square both sides of this.
d%5E2+=+53
The equation for your circle is:
%28x%2B3%29%5E2+%2B+%28y-4%29%5E2+=+53

Answer by askmemath(368) About Me  (Show Source):
You can put this solution on YOUR website!
Equatation of a circle with centre (a,b) and radius r is given by (x-a)^2+(y-b)^2=r^2
You are given the centre (a,b) as (-3,4) .You are also given a point that lies on the circle.The distance between this point and the centre is the radius