Question

Area of the triangle formed by 2x^2 + xy + 3y^2 = 0 and x + y 3 is ?

Answer 1

As you likely know, a triangle is formed by three straight lines. I note that you have the quadratic 2x^2 in this problem. A quadratic has a parabolic graph.

My suggestion: Solve the given set of equations for x and y. You have 2 equations in 2 unknowns, so should be able to do that.

You will likely find that the resulting graph encloses an area, but that this area is not a triangle.

Instead, identify the coordinates of each of the 3 points of intersection of these graphs.

Plot these 3 points.

Connect these 3 points with straight lines.

Find the area of the resulting triangle. Show your work.

Answer 2

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