5.1.1.1: A.1.1- Introduction to Quadratic Equations with Two Variables
- Page ID
- 100224
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A quadratic equation with two variables \(x\) and \(y\) is an equation that is equivalent to
\[Ax^2+By^2+Cx+Dy+Exy+F=0,\]
where at least one of \(A\) or \(B\) is not zero.
In general, the graphs of the solution to this type of equation is called a conic section (a circle, parabola, ellipse, hyperbola, line, two intersecting lines, or a point).
We will discuss the solutions to this type of equation in certain cases. We'll begin with the case that \(A=E=0\) or \(B=E=0\). The solutions to these equations are called parabolas.
We will then discuss the case where \(A=B\) and \(E=0\) in which case, the graph is a circle.
The other cases could be treated in a similar way.