PQ is a chord of the circle $$x2+y2$$−$$2x$$−$$8=0$$ whose midpoint is (2$$, $$2). The circle passing through P, Q and (1$$, $$2) is

Question

PQ is a chord of the circle $$x2+y2$$−$$2x$$−$$8=0$$ whose midpoint is (2$$, $$2). The circle passing through P, Q and (1$$, $$2) is

Infinity Learn · Accepted Answer

The equation of the chord of the circle $$x2+y2$$−$$2x$$−$$8=0$$ having (2$$, $$2) as its $$mid-point$$ $$is2x+2y$$−(x+2)−$$8=4+4$$−$$4$$−$$8$$                     [Using: S′$$=T$$ ] ⇒$$x+2y$$−$$6=0$$ The equation of a circle passing through P and Q $$isx2+y2$$−$$2x$$−$$8+$$λ(x+2y$$−$$6)=0$$                       ... $$(i)It$$ passes through $$(1$$, $$2).∴ $$1+4$$−$$2$$−$$8+$$λ(1+4$$−$$6)=0$$⇒λ$$=$$−$$5Putting$$ the value of λ in $$(i), we $$obtainx2+y2$$−$$7x$$−$$10y+22=0as$$ the equation of the required circle.

PQ is a chord of the circle $x^{2} + y^{2} - 2 x - 8 = 0$ whose midpoint is (2, 2). The circle passing through P, Q and (1, 2) is

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PQ is a chord of the circle x2+y2−2x−8=0 whose midpoint is (2, 2). The circle passing through P, Q and (1, 2) is

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PQ is a chord of the circle $x^{2} + y^{2} - 2 x - 8 = 0$ whose midpoint is (2, 2). The circle passing through P, Q and (1, 2) is