Geo4.14

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Find the equation to the circle on the line segment joining the following points as diameter i).(5,1),(7,5)\, ii).(-4,-2),(1,1)\,


i). Equation of the circle with diametric ends as (5,1),(7,5) is

(x-5)(x-7)+(y-1)(y-5)=0\,

x^{2}-7x-5x+35+y^{2}-5y-y+5=0\,

x^{2}+y^{2}-12x-6y+40=0\,


ii). Equation of the circle with diametric ends as (-4,-2),(1,1) is

(x-(-4))(x-1)+(y-(-2))(y-1)=0\,

(x+4)(x-1)+(y+2)(y-1)=0\,

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

x^{2}+y^{2}+3x+y-6=0\,


Main page:Geometry:Circles