SOLUTION: Part a) Given three noncollinear points,construct the circle and then write the equation of the circle. The points are A(12,-1),B(6,-3),C(4,3) Part b) Using the equation and

Question 329434: Part a) Given three noncollinear points,construct the circle and then write the equation of the circle.
The points are A(12,-1),B(6,-3),C(4,3)
Part b) Using the equation and graph of the circle above,determine if the following lines are tangent,secant, or neither.
y=1
y=2x-1
Found 2 solutions by Fombitz, Alan3354:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
a)

1.

2.

3.
Equate eq. 1 and eq. 2,

4.
Equate eq. 1 and eq. 3,

5.
Add eq. 4 and eq. 5 to eliminate k.

Then use either eq. 4 or 5 to solve for h.

Finally solve for R,

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b)
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Circle, points, and two lines plotted.
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Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Use determinants.
|x^2 + y^2 +x +y +1|
x1^2+y1^2 x1 y1 +1|
x2^2+y2^2 x2 y2 1| = 0
x3^2+y3^2 x3 y3 1|
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(x1,y1), etc are the 3 points.
It looks messy, but I made an Excel sheet that does them.
It also does parabolas.
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