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Question

The pair of lines represented by 3ax2+5xy+(a22)y2=0 are perpendicular to each other for

A
two values of a
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B
for all values of a
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C
for one value of a
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D
for no value of a
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Solution

The correct option is A two values of a
3ax2+5xy+(a22)y2=0 are perpendicular to each other

coefficient of x2+coefficient of y2=0

3a+a22=0

a2+3a2=0

a=3±9+82

so a=3+172 and a=3172

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