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Question

Find the combined equation of the images of the pair of lines represented by ax2+2hxy+by2=0 in the line mirror y=0.

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Solution

Let the given lines be y=m1x,y=m2x where
m1=tanθ1,m2=tanθ2
The image of y=m1x about y=0 i.e., axis of
x will make an angle θ1 with xaxis
and hence its equation is y=tan(θ1)x
or y=tanθ1x or y+m1x=0
Combined equation is
(y+m1x)(y+m2x)=0
or y2+xy(m1+m2)+m1m2x2=0
or by22hxy+ay2=0

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