The equation `x-y=4 and x^2+4xy+y^2=0` represent the sides of

Options

A. an equilateral triangle
B. a right angled triangle
C. an isosceles triangle
D. None of these

Answer

A

Explanation

Acute angle between the lines `x^2+4xy+y^2=0` is `tan^2(2sqrt(4-1))//(1+1)=tan^(-1)sqrt(3)=tan^(-1)pi//3`. Angle bisectors of `x^2+4xy+y^2=0` are given by `(x^2-y^2)/(1-1)=(xy)/(2)`
`x^2-y^2=0rArr x=+-y`
As `x+y=0` is perpendicular to `x-y=4`, so the given triangle is equilateral triangle.