Geo4.131

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Find the equation of the circle belonging to the coaxal system of which the limiting points are (2,-3),(0,-4)\, and which passes through (2,-1)

Equations to the circles for the given limiting points are

(x-2)^{2}+(y+3)^{2}=0,(x-0)^{2}+(y+4)^{2}=0\,

x^{2}+y^{2}-4x+6y+13=0,x^{2}+y^{2}+8y+16=0\,

Equation to the adical axis is

-4x-2y-3=0,4x+2y+3=0\,

Equation to the coaxal system is

x^{2}+y^{2}-4x-6y+13+k(4x+2y+3)=0\,

This circle passes through (2,-1)

Then,

4+1-8+6+k(9)=0,9k=3.k={\frac  {1}{3}}\,

Therefore the required equation is

3(x^{2}+y^{2})-8x-16y40=0\,


Main Page:Geometry:Circles