Apollonius of Perga (about 262 BC - about 190 BC) was a Greek geometer, noted for his writings on conic sections. It was Apollonius who gave the ellipse, the parabola, and the hyperbola the names by which we know them.
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... this means that the parabola described by the quadratic equation touches the x-axis in a single point.)
If the discriminant is positive, then there are two ...