Geo4.30

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Find the equation to the circle on AB as diameter and hence find the circle passing through A(3,4),B(3,-6),C(-1,2)\,

Equation of the circle with AB as diameter is

(x-3)(x-3)+(y-4)(y+6)=0\,

x^{2}-6x+9+y^{2}+2y-24=0\,

x^{2}+y^{2}-6x+2y-15=0\,

Equation of the circle passing through A,B,C is

Let the equation be x^{2}+y^{2}+2gx+2fy+c=0\,

It passes thro'(3,4)

6g+8f+c=25\,

It passes thro'(3,-6)

6g-12f+c=-45\,

It passes thro'(-1,2)

-2g+4f+c=-5\,

Solving first two

20f=20,f=1\,

Solving second two,

4c=-60,c=-15\,

Now

6g-12(1)-15=-45,6g=-18,g=-3\,

Hence the equation is

x^{2}+y^{2}-6x+2y-15=0\,

Main Page:Geometry:Circles