In mathematics, parametric equations are a method of expressing a set of related quantities as explicit functions of a number of independent variables, known as " parameters . " For example, rather than a function relating variables " x " and " y " in a Cartesian coordinate system such as y = f ( x ), a parametric equation describes a position along the curve at time " t " by x = g ( t ) and y = h ( t ).
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One way to visualize that it's a parabola rather than a hyperbola without finding the explicit function is to consider what happens when you continue drawing lines past where you stopped : ( 0, 0 ) to ( 0, a + 1 ), (-1, 0 ) to ( 0, a + 2 ), . . . (-n, 0 ) to ( 0, a + 1 + n ), . . . The slope of these lines go through the vertical and approach 1.
