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Q.

The combined equation 5x2+4xy−5y2=0represents the pair of lines and those lines are

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a

Perpendicular

b

Parallel

c

Coincide

d

one makes angle 45°with other line

answer is A.

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Detailed Solution

If the equation ax2+2hxy+by2=0 represents a pair of perpendicular lines then a+b=0For the equation 5x2+4xy−5y2=0,a+b=−5+5=0Therefore, the equation 5x2+4xy−5y2=0represents a pair of perpendicular lines passing through the origin.
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The combined equation 5x2+4xy−5y2=0represents the pair of lines and those lines are