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

locus of the centre of circles touching angle bisectors of the pair of lines ax2+bxy+ay2=0is..............???


    (answer--xy=0)

Grade:11

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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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Badiuddin


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