Parameter Exploration of Bivariate Quadratic Inequality x²+2xy+y²+5x+ay+b>0

2016-01-14 04:50
This GeoGebra example investigates the solution set of the bivariate quadratic inequality x² + 2xy + y² + 5x + ay + b > 0 and its dependence on parameters a and b. Since x² + 2xy + y² = (x+y)², the inequality can be rewritten as (x+y)² + 5x + ay + b > 0, combining a perfect square with linear terms. Through dynamic geometric construction, it visualizes how the solution region in the coordinate pla