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Question

The equation x- y = 4 and x2+4xy+y2=0 represent the sides of


A

an equilateral triangle

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B

a right angled triangle

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C

an isosceles triangle

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D

none of these

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Solution

The correct option is A

an equilateral triangle


Acute angle between the lines x2+4xy+y2=0 is
tan12411+1=tan1 3=π3
Angle bisectors of x2+4xy+y2=0 are given by
x2y211=xy2 x2y2=0 x=±y
As x + y = 0 is perpendicular to x - y = 4, the given triangle is isosceles with vertical angle equal to π3 and hence it is equilateral.


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