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Question

One bisector of the angle between the lines given by a(x−1)2+2h(x−1)y+by2=0 is 2x + y - 2 = 0.The other bisector is


A

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B

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C

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D

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Solution

The correct option is D


We have a(x−1)2+2h(x−1)y+by2=0

or a(x−1)2+2h(x−1)(y−0)+b(y−0)2=0

This equation represents a pair of straight lines intersecting at (1,0).Therefore shifting the origin at (1,0),we have x = X + 1, y = Y + 0 and the equation reduces to aX2+2hXY+bY2=0..............(i)

One of the bisector of the angles between the lines given by (i) is 2x + y - 2 = 0 or 2(X + 1) + y - 2 = 0 i.e. 2X + Y = 0.Since the bisector are always at right angle , therefore the other bisector is X - 2Y = 0

i.e., x - 1 - 2y = 0 or x - 2y - 1 = 0.


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