Area of a triangle formed by the lines x 2 +4xy+y 2 =0 and x+y=1 is

The given equation x^2 + 4xy + y^2 = 0 can be rewritten as (x + 2y)^2 = 0. This implies that x = -2y.

So, we have two lines forming the triangle: x = -2y and x + y = 1.

We can find the intersection points of these lines by setting them equal to each other:

-2y = 1 - y => y = 1

Substitute y = 1 into x + y = 1, we get x = 0.

So, the intersection point is (0, 1).

The other intersection point is the y-intercept of the line x + y = 1, which is (0, 1).

The base of the triangle is the distance between these two points, which is 1.

The height of the triangle is the y-coordinate of the intersection point, which is also 1.

The area of the triangle is given by the formula 1/2 * base * height = 1/2 * 1 * 1 = 0.5 square units.