SOLUTION: Find an equation of the circle with center at(-8,7) and passing through(1,-4) in the form of {{{(x-a)^2+(y-B)^2=C}}} where A,B,C are constant. Then A= B= C= Ive alread

Algebra ->  Rational-functions -> SOLUTION: Find an equation of the circle with center at(-8,7) and passing through(1,-4) in the form of {{{(x-a)^2+(y-B)^2=C}}} where A,B,C are constant. Then A= B= C= Ive alread      Log On


   

Question 160196: Find an equation of the circle with center at(-8,7) and passing through(1,-4) in the form of %28x-a%29%5E2%2B%28y-B%29%5E2=C where A,B,C are constant. Then
A=
B=
C=
Ive already have the answers for A B they are -8,7 I just how to find C if the radius is not provided
Found 2 solutions by Edwin McCravy, nerdybill:
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation of the circle with center at(-8,7) and passing through (1,-4) in the form of %28x-A%29%5E2%2B%28y-B%29%5E2=C where A,B,C are constant. Then
A=
B=
C=
Ive already have the answers for A, B they are -8,7. I just
want to know how to find C if the radius is not provided.

So instead of:

%28x-A%29%5E2%2B%28y-B%29%5E2=C

write

%28x-%28-8%29%29%5E2%2B%28y-%287%29%29%5E2=C

%28x%2B8%29%5E2%2B%28y-7%29%5E2=C

Think now: What haven't you used that was given?

Answer:  You haven't used this: "passing through (1,-4)"

So that means if you substitute (x,y) = (1,-4), the equation
must be true.  So let's substitute that:

%28x%2B8%29%5E2%2B%28y-7%29%5E2=C
%28%281%29%2B8%29%5E2%2B%28%28-4%29-7%29%5E2=C
%281%2B8%29%5E2%2B%28-4-7%29%5E2=C
%289%29%5E2%2B%28-11%29%5E2=C
81%2B121=C
202=C

So write 202 for C

%28x%2B8%29%5E2%2B%28y-7%29%5E2=202

and you're done. The radius is sqrt%28202%29.

Edwin

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation of the circle with center at(-8,7) and passing through(1,-4) in the form of %28x-a%29%5E2%2B%28y-B%29%5E2=C where A,B,C are constant.
Then
A= -8
B= 7
C=
.
Recapping you have the center and you're given a point (1, -4) -- simply plug it in and solve for C:
%28x-a%29%5E2%2B%28y-B%29%5E2=C
%281-%28-8%29%29%5E2%2B%28-4-7%29%5E2=C
9%5E2%2B%28-11%29%5E2=C
81%2B121=C
202=C
.
A= -8
B= 7
C= 202
and
%28x-a%29%5E2%2B%28y-B%29%5E2=C
%28x-%28-8%29%29%5E2%2B%28y-7%29%5E2=202
%28x%2B8%29%5E2%2B%28y-7%29%5E2=202