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Question

Angle between the line joining the origin to the points of intersection of the curves 2x2+3y2+10x=0 and 3x2+5y2+16x=0 is


A

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B

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C

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D

None of these

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Solution

The correct option is C


The equation of any curve through the points of intersection of the given curves is 2x2+3y2+10x+λ(3x2+5y2+16x)=0) ....(i)

If this equation represents two straight lines through the origin, then this must be homogeneous equation of second degree i.e., coefficient of x in (i) must vanish

10+16λ=0=1016=58

Substituting this value of λ in (i), we get the equation of pair of straight lines x2y2=0 .............(ii)

Hence the lines represented by the equation (ii) are mutually perpendicular.


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