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Q.

The equation of the pair of straight lines through the point 1,1 and  perpendicular to the pair of lines and perpendicular to the pair of lines 3x28xy+5y2=0 is

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a

5x2+8xy+3y214x18y+16=0

b

5x28xy+3y218x14y+32=0

c

5x2+8xy+3y218x14y+16=0

d

5x28xy+3y214x18y+32=0

answer is B.

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Detailed Solution

GivenEquation3x28xy+5y2=01Comparingwithax2+2hxy+by2=0a=3,h=4,b=5Equationofthelinepassingthrough1,  1andr  to1isbxx122hxx1yy1+yy12=05x12+8x1y1+3y12=05x2+12x+8xyxy+1+3y2+12y=05x2+510x+8xy8x8y+8+3y2+36y=05x2+8xy+3y218x14y+16=0

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