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The two lines represented by $3 {ax}^{2} + 5 xy + (a^{2} - 2) y^{2} = 0$ are perpendicular to each other for

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two values of a

for one value of a

for no value a

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detailed solution

Correct option is A

3a+a2−2=0 or a2+3a−2=0 or a=−3±9+82=−3±172Therefore, there are two values of a.

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The two lines represented by 3ax2+5xy+(a2−2)y2=0 are perpendicular to each other for

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The two lines represented by $3 {ax}^{2} + 5 xy + (a^{2} - 2) y^{2} = 0$ are perpendicular to each other for