The equation of the circle passing through (0$$, $$0) and belonging to the system of circles of which (3$$, $$1) and $$(-1$$, $$5)$$ are limiting points, is

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Infinity Learn · Accepted Answer

Circles $$having($$ $$3$$, $$1)$$ and $$(-1$$, $$5)$$ as limiting pointsare $$S1$$≡(x$$−$$3)2+(y$$−$$1)2=0$$ and $$S2$$≡$$(x+1)2+(y$$−$$5)2=0The$$ equation of the family of circles $$isS1+$$λ$$S1$$−$$S2=0$$⇒ $$(x$$−$$3)2+(y$$−$$1)2+$$λ$$($$−$$8x+8y$$−$$16)=0$$                              ... $$(i)It$$ passes through $$(0$$, $$0).∴ $$10$$−$$16$$λ$$=0$$⇒λ$$=58Substituting$$ the value of λ in (i), we $$getx2+y2$$−$$11x+3y=0$$ as the equation of the required circle.

The equation of the circle passing through (0, 0) and belonging to the system of circles of which (3, 1) and (-1, 5) are limiting points, is

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