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

Algebra ->  Circles -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
a)%28h-12%29%5E2%2B%28k%2B1%29%5E2=R%5E2
h%5E2-24h%2B144%2Bk%5E2%2B2k%2B1=R%5E2
1.h%5E2%2Bk%5E2-24h%2B2k%2B145=R%5E2
%28h-6%29%5E2%2B%28k%2B3%29%5E2=R%5E2
h%5E2-12h%2B36%2Bk%5E2%2B6k%2B9=R%5E2
2.h%5E2%2Bk%5E2-12h%2B6k%2B45=R%5E2
%28h-4%29%5E2%2B%28k-3%29%5E2=R%5E2
h%5E2-8h%2B16%2Bk%5E2-6k%2B9=R%5E2
3.h%5E2%2Bk%5E2-8h-6k%2B25=R%5E2
Equate eq. 1 and eq. 2,
h%5E2%2Bk%5E2-24h%2B2k%2B145=h%5E2%2Bk%5E2-12h%2B6k%2B45
-24h%2B2k%2B145=-12h%2B6k%2B45
-12h-4k=-100
4.3h%2Bk=25
Equate eq. 1 and eq. 3,
h%5E2%2Bk%5E2-24h%2B2k%2B145=h%5E2%2Bk%5E2-8h-6k%2B25=R%5E2
-24h%2B2k%2B145=-8h-6k%2B25
-16h%2B8k=-120
5.2h-k=15
Add eq. 4 and eq. 5 to eliminate k.
3h%2Bk%2B2h-k=25%2B15
5h=40
highlight%28h=8%29
Then use either eq. 4 or 5 to solve for h.
16-k=15
highlight%28k=1%29
Finally solve for R,
%28h-12%29%5E2%2B%28k%2B1%29%5E2=R%5E2
%288-12%29%5E2%2B%281%2B1%29%5E2=R%5E2
16%2B4=R%5E2
R=sqrt%2820%29
highlight%28R=2sqrt%285%29%29
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highlight_green%28%28x-8%29%5E2%2B%28y-1%29%5E2=20%29
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b)
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Circle, points, and two lines plotted.
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Answer by Alan3354(69443) About Me  (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.