A portion of a parabola is defined by the parametric equations x = 2 − (t + 1)^2, y = t + 2 with −3 ≤ t ≤ 0.
(a) Eliminate the parameter t to determine the equation of the curve in terms of only x and y.
(b)sketch the graph of the parametric curve only for −3 ≤ t ≤ 0. Use arrows to indicate the direction of increasing t.

Question

A portion of a parabola is defined by the parametric equations x = 2 − (t + 1)^2, y = t + 2 with −3 ≤ t ≤ 0.
(a) Eliminate the parameter t to determine the equation of the curve in terms of only x and y.
(b)sketch the graph of the parametric curve only for −3 ≤ t ≤ 0. Use arrows to indicate the direction of increasing t.

anonymous · Answer

Clearly:$$
y=t+2\implies y-2= t
$$Thus we get: $$
x = 2 − (t + 1)^2 \implies x = 2 − ((y-2)+ 1)^2
$$