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Question

If (a+b)2=4h2, prove that one of the lines given by the equation ax2+2hxy+by2=0 will bisect the angle between the co-ordinate axes.

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Solution

Solution:-
The equation of the bisectors of the angles between the coordinate axes are y=x and y=x.

Let y=x belong to ax2+2hxy+by2=0

ax2+2hx2+bx2=0

a+b=2h.....(1)

If y=x belongs to ax2+2hxy+by2=0.

ax22hx2+bx2=0

a+b=2h.....(2)

From eqn(1)&(2), we have

(a+b)=±2h

Squaring both sides, we get

(a+b)2=4h2

Hence proved.

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