SOLUTION: Find the equation of the circle that passes through (4,2) and (-6,-2), centre on the y-axis.

Algebra ->  Circles -> SOLUTION: Find the equation of the circle that passes through (4,2) and (-6,-2), centre on the y-axis.      Log On


   

Question 1079002: Find the equation of the circle that passes through (4,2) and (-6,-2), centre on the y-axis.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So use the general equation of the circle,
%28x-h%29%5E2%2B%28y-k%29%5E2=R%5E2
Since you know the center is on the y-axis, then h=0
x%5E2%2B%28y-k%29%5E2=R%5E2
So using the two points,
4%5E2%2B%282-h%29%5E2=R%5E2
16%2B%282-h%29%5E2=R%5E2
and
%28-6%29%5E2%2B%28-2-h%29%5E2=R%5E2
36%2B%28-2-h%29%5E2=R%5E2
Setting them equal to each other,
16%2B%282-h%29%5E2=36%2B+%28-2-h%29%5E2+
16%2B4-4h%2Bh%5E2=36%2B4%2B4h%2Bh%5E2
-8h=20
h=-20%2F8
h=-5%2F2
So then use either point to solve for R.
16%2B%282-%28-5%2F2%29%29%5E2=R%5E2
16%2B%284%2F2%2B5%2F2%29%5E2=R%5E2
16%2B%289%2F2%29%5E2=R%5E2
64%2F4%2B81%2F4=R%5E2
R%5E2=145%2F4
So then,
highlight%28x%5E2%2B%28y%2B5%2F2%29%5E2=145%2F4%29
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