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Question

If y = mx be one of the bisectors of the angle between the lines ax22hxy+by2=0, then


A

h(1m2)+m(ab)=0

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B

h(1m2)+m(a+b)=0

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C

h(1m2)+m(ab)=0

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D

h(1+m2)+m(a+b)=0

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Solution

The correct option is C

h(1m2)+m(ab)=0


Here equation of one bisector of angle is y - mx = 0, therefore equation of second is x + my = 0.

Hence combined equation is (x + my)(y - mx) = 0

mx2xy(m21)+my2=0 ....................(i)

Also equation of bisectors of ax22hxy+by2=0 is

hx2(ab)xy+hy2=0 ................(ii)

Hence (i) and (ii) are the same equations , therefore

mh=m21(ab)h(m21)=m(ab)

m(ab)+h(1m2)=0


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