Find the equation of the smallest circle passing through the
intersection of the line `x+y=1`
and the circle `x^2+y^2=9`
Text Solution
Verified by Experts
Let the given circle and line intersect at points A and B. Equation of family of cirlces through A and B is `x^(2)+y^(2)-9+lambda(x+y-1)=0,lambda in R` Variable centre of the circle is `(-(lambda)/(2),-(lambda)/(2))`. The smallest circle of this family is that for which A and B are end points of diameter. So, centre `(-(lambda)/(2),-(lambda)/(2))`. lies ont he chord `x+y-1=0`. `implies -(lambda)/(2),-(lambda)/(2)-1=0` `implies lambda= -1` Using this value for `lambda`, the equation of the smallest circle is `x^(2)+y^(2)-9-(x+y-1)=0` or `x^(2)+y^(2)-x-y-8=0`
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