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Question

The line joining the origin to the points of intersection of the curves ax2+2hxy+by2+2gx=0 and ax2+2hxy+by2+2gx=0 will be mutually perpendicular, if


A

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B

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C

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D

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Solution

The correct option is B


The family of lines passing through point of intersection of the given curves will be

ax2+2hxy+by2+2gx=0λ(ax2+2hxy+by2+2gx)=0 (a+aλ)x2+(2h+2hλ)xy+(b+bλ)y2+(2g+2gλ)x=0

Now the condition for perpendicularity is =0 and a + b = 0.

a+aλ+b+bλ=0λ=a+ba+b

and =abc+2fghaf2bg2ch2=0

0+00(b+bλ)(2g+2gλ)20=0

4(b+bλ)(g+gλ)2=0

Now on putting the value of λ, we get

g(a+b)=g(a+b).


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