Q.

A triangle is formed by the lines whose combined equation is given by (x+y-4)(x y-2 x-y+2)=0. The equation of its circumcircle is

Moderate

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x2+y2−5x−3y+8=0

x2+y2−3x−5y+8=0

x2+y2+2x+2y−3=0

None of the above

answer is 2.

(Detailed Solution Below)

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Detailed Solution

(x+y−4)(xy−2x−y+2)=0 (x+y−4)(x−1)(y−2)=0 ∵ AB⊥ACtherefore B C is diameter, then equation of circumcircle is ⇒(x−2)(x−1)+(y−2)(y−3)=0⇒x2+y2−3x−5y+8=0

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