locus of the centre of circles touching angle bisectors of the pair of lines ax2+bxy+ay2=0is..............???(answer--xy=0)

Dear shivanshi

ax2+bxy+ay2=0

equation of the bisector of hese lines are

(x² -y²) /(a-a) =xy/(b/2)

or

x² -y²=0

y =x or y=-x

clearly these lines are symmetric about y axis and x axis

so if a circle touches both these two lines then its center must lie either on x axis or in y axis

so locus are  x=0

           and    y=0

 combine equation  is xy=0

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