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Question

The x-intercept of angle bisector of angle between the lines 2x+y2=0 and 2x+4y+7=0 which contains the fixed point on the family of lines (2cosα+3sinα)x+(3cosα5sinα)y=5cosα2sinα for different values of α, is equal to

A
112
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B
112
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C
12
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D
12
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Solution

The correct option is A 112
Family of lines cosα(2x+3y5)+sinα(3x5y+2)=0 will pass through fixed point i.e., point of intersection of 2x+3y5=0 and 3x5y+2=0 which is (1,1)

21+12>0 and 21+41+7>0
Angle bisector
2x+y25=+(2x+4y+725) will contain the point (1,1)
4x+2y4=2x+4y+7
2x2y11=0

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