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Question

The lines (lx+my)23(mxly)2=0 and lx + my + n = 0 form


A

An isosceles triangle

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B

A right angled triangle

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C

An equilateral triangle

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D

concurent lines

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Solution

The correct option is C

An equilateral triangle


Lines are

[(l+3m)x+(m3l)y][(l3m)x+(m+3l)y] = 0

and L3=lx+my+n=0.L1andL2.are above two lines.

S1=(l+3m)(ml),S2=(l3m)(m+l),S3=1m

(Where S1,S2andS3 are slopes of the lines)

θ13=tan1(l+3mm3l)+lm1+(l+3mm3l)lm

= tan1(3m23l2l2+m2)=60

θ25=tan1(l3mm+3l)+lm1+(l3mm+3l)lm

= tan1(3m2+3l2m2+l2)=tan1(3)=60

Hence, triangle is equilateral.

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