SOLUTION: The center of a circle is on the line x + 2y = 4 The circle passes through points A (6,9) and B (12,-9) Write the equation of the circle. sq. root ((9-(-x/2+2)^2 + (6-x)^2 ) -

Algebra ->  Coordinate-system -> SOLUTION: The center of a circle is on the line x + 2y = 4 The circle passes through points A (6,9) and B (12,-9) Write the equation of the circle. sq. root ((9-(-x/2+2)^2 + (6-x)^2 ) -       Log On


   

Question 166772: The center of a circle is on the line x + 2y = 4 The circle passes through points A (6,9) and B (12,-9) Write the equation of the circle.
sq. root ((9-(-x/2+2)^2 + (6-x)^2 ) - sq. root ((-9-(-x/2+2)^2 + (12-x)^2) = 0
x=100, y=-48 But these numbers don't check
Thanks in advance,
Mark
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
is correct, however express it this way:



Now square both sides:



Collect terms:

%287%2B%28x%2F2%29%29%5E2%2B%286-x%29%5E2=%28-11%2B%28x%2F2%29%29%5E2%2B%2812-x%29%5E2

Expand the binomials:



The 2nd degree terms fall out:



49+%2B+7x+%2B+36+-+12x+=+121+-+11x+%2B+144+-+24x

Collect terms:

30x=180

x=6 so y=-x%2F2%2B2=-3%2B2=-1, hence center at (6,-1)

Radius squared: %289%2B1%29%5E2%2B%286-6%29%5E2=100

Equation: %28x-6%29%5E2%2B%28y%2B1%29%5E2=100