Determine if (11,9) is on the graph. We know the answer should be no. Using the y-equation first, if y = 9 then t = 3. Then
x = (3)2 + 1 = 10.
Since x≠ 11 at the only t-value that makes y = 9, the point (11,9) is not on the graph.
It's also possible to determine the points at which parametric equations intersect. This is how we'd know if Mario ran into a red koopa flying loftily over the canyon during his jump. One example is given here.