One of the bisectors of the angle between the lines a(x−1)2+2h(x−1)(y−2)+b(y−2)2=0 is x+2y−5=0. Then value of b−ah is________
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answer is 1.5.
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Detailed Solution
Shifting the origin to (1, 2), the equation of given pair of lines becomes ax2+2xhy+by2=0 whose one angle bisector is x+2y=0 (given) and other is 2x−y=0.∴ Combined equation of angle bisector is (x+2y)(2x−y)=0 On comparing with x2−y2a−b=xyh,we get a−b=−3 and h=2∴b−ah=32