One of the limit point of the coaxial system of circles containing $$x2+y2$$−$$6x$$−$$6y+4=0$$,$$x2+y2$$−$$2x$$−$$4y+3=0$$, is

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One of the limit point of the coaxial system of circles containing $$x2+y2$$−$$6x$$−$$6y+4=0$$,$$x2+y2$$−$$2x$$−$$4y+3=0$$, is

Infinity Learn · Accepted Answer

The equation of the family of coaxial system of circles haveing $$x2+y2$$−$$6x$$−$$6y+4=0$$ and $$x2+y2$$−$$2x$$−$$4y+3=0$$ two members $$isx2+y2$$−$$6x$$−$$6y+4+$$λ$$($$−$$4x$$−$$2y+1)=0$$⇒ $$x2+y2$$−$$2x(3+2$$λ$$)$$−$$2y(3+$$λ$$)+4+$$λ$$=0Coordinates$$ of centre of circle  (i) are⁡(3+2$$λ,$$3+$$λ$$).1Radius$$ $$=(3+2$$λ$$)2+(3+$$λ$$)2$$−$$(4+$$λ$$)For$$ limiting points, we must haveRadius $$=0$$⇒$$5$$λ$$2+17$$λ$$+14=0$$⇒λ$$=$$−$$2$$,−$$7/5Hence$$, limiting points are $$($$−$$1$$,$$1) and (1/5$$,$$8/5)

One of the limit point of the coaxial system of circles containing $x^{2} + y^{2} - 6 x - 6 y + 4 = 0, x^{2} + y^{2} - 2 x - 4 y + 3 = 0,$ is

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One of the limit point of the coaxial system of circles containing x2+y2−6x−6y+4=0,x2+y2−2x−4y+3=0, is

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One of the limit point of the coaxial system of circles containing $x^{2} + y^{2} - 6 x - 6 y + 4 = 0, x^{2} + y^{2} - 2 x - 4 y + 3 = 0,$ is