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If one of the lines given by the equation $2 x^{2} + a x y + 3 y^{2} = 0$ coincide with one of those given by $2 x^{2} + b x y - 3 y^{2} = 0$ and the other lines represented by them be perpendicular, then

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a = – 5, b = 1

a = 5, b = – 1

a = 5, b = 1

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detailed solution

Correct option is C

Let 23x2+a3xy+y2=(y−mx)y−m′xand 2−3x2+b−3xy+y2=y+1mxy−m′xthen m+m′=−a3,mm′=23 (i)1m−m′=−b3,−m′m=−23⇒m2=1⇒m=±1If m=1,m′=23⇒a=−5,b=−1If m=−1,m′=−23⇒a=5,b=1.

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If one of the lines given by the equation 2x2+axy+3y2=0 coincide with one of those given by 2x2+bxy−3y2=0 and the other lines represented by them be perpendicular, then

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If one of the lines given by the equation $2 x^{2} + a x y + 3 y^{2} = 0$ coincide with one of those given by $2 x^{2} + b x y - 3 y^{2} = 0$ and the other lines represented by them be perpendicular, then