Geo4.117

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Find the equation to the circle which is orthogonal to each of x^{2}+y^{2}+2x+17y+4=0,x^{2}+y^{2}+7x+6y+11=0,x^{2}+y^{2}-x+22y+3=0\,

Let the given circles be 1,2,3

Now the radical axis of 1 and 2,2 and 3 are

-5x+11y-7=0,8x-16y+8=0\,

5x-11y+7=0,x-2y+1=0\,

Solving these two,

x=3,y=2\,. Hence the radical centre.

Length of the tangent from (3,2) to the circle 1 is

{\sqrt  {3^{2}+2^{2}+6+34+4}}={\sqrt  {57}}\,

Therefore the equation of the circle with centre (3,2) and the radius {\sqrt  {57}}\, is

(x-3)^{2}+(y-2)^{2}=57\,

x^{2}+y^{2}-6x-4y-44=0\,


Main Page:Geometry:Circles