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Question

ax2+2hxy+by2=0 represents a pair of straight lines through origin & angle between them is given by
tanθ=2h2aba+b. If the lines are perpendicular then a+b=0 and the equation of bisectors is given by x2y2ab=xyh
The general equation of second degree given by
ax2+2hxy+by2+2gx+2fy+c=0 represent a pair of straight lines if =0 or
∣ ∣ahghbfgfc∣ ∣=0 or abc+2fghaf2bg2ch2=0
On the basis of above information answer the following question
The Joint equation of the bisectors of the angle between the lines represented by ax2+2hxy+by2=0 is

A
a pair of perpendicular lines
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B
a pair of parallel lines
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C
a pair of intersecting lines but not er
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D
None of these
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Solution

The correct option is B a pair of perpendicular lines
Equation of bisectors of angle between the pair of straight line ax2+2hxy+by2=0 is given by x2y2ab=xyh

hx2(ab)xyhy2=0

Here coefficient of x2+ coefficient of y2=h+(h)=0

above equation represent the pair of er lines

Hence choice (a) is correct.

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