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Q.

The equations a2x2+2h(a+b)xy+b2y2=0 and ax2+2hxy+by2=0

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a

two pairs of perpendicular straight lines

b

two pairs of parallel straight lines

c

two pairs of straight lines which are equally inclined to each other

d

None of these

answer is A.

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Detailed Solution

The given equations are  a2x2+2h(a+b)xy+b2y2=0______(1)and ax2+2hxy+by2=0_____(2)The equation of the bisectors of the angles between the lines represented by (1) is x2−y2a2−b2=xyh(a+b)or x2−y2a−b=xyh which is the same as the equation of bisectors of the angles between the line pair (2). Thus, two line pairs are equally inclined to each other.
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