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 linens `x^(2)+4xy+y^(2)=0` is
`tan^(-1){(2sqrt(4-1))//(1+1)}=tan^(-1)sqrt(3)=pi//3`. the angle bisectors of `x^(2)+4xy+y^(2)=0`are given by
`(x^(2)-y^(2))/(1-1)=(xy)/(2)`
or `x^(2)-y^(2)=0orx=+-y`
As `x+y=0` is perpendicular to `x-y=4` , the given triangle is isosceles with vertical angle equal to `pi//3`. Hence , it is an equilateral triangle.