Find the equation of the circle passing through the points P(1,1) , Q(2,-1) and R(3,2)
Answer (1)
18th Nov, 2020
Hello There,
The general equation of a circle is given as :
x^2 + y^2 +2gx + 2fy + c = 0
Now if the circle passes through these three points then obviously these three points satisfy the equation of circle. So
For point P , we have
1+1+2g+2f+c=0 (eqn.1)
for point Q, we have
4+1+4g-2f+c=0 (eqn 2)
for point R, we have
9+4+6g+4f+c =0 (eqn 3)
Solving these three equation we get that ;
g = -5/2 f = -1/2 and c = 4
So the equation of circle is given by, putting the values of f, g and c in the general eqn of circle.
eqn = x^2 + y^2 - 5x - y + 4=0
Hope this helps.
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