Equations expressing x and y in terms of a third variable (parameter), often 't'.

A circle described by equations using a parameter to show movement around it.

A line described by equations using a parameter to show movement along it.

Time, indicating how the (x, y) point moves as 't' changes.

A vector that indicates the direction of the line segment, calculated from two points.

A value between 0 and 1 that determines the position along the line segment.

$x(t) = cos(t)$, $y(t) = sin(t)$

$0 \le t \le 2\pi$

$x(t) = a + rcos(t)$, $y(t) = b + rsin(t)$

$x(t) = cos(t + c)$, $y(t) = sin(t + c)$

$x = x_1 + k(x_2 - x_1)$, $y = y_1 + k(y_2 - y_1)$, where $0 \le k \le 1$

Substitute the extreme values of the parameter (usually 0 and 1) into the parametric equations for x and y.

1. Identify the center (a,b) and radius r from the equations x(t) = a + rcos(t) and y(t) = b + rsin(t). 2. Write the equation in the form (x-a)^2 + (y-b)^2 = r^2.

Use the trigonometric identity $cos^2(t) + sin^2(t) = 1$. Solve for cos(t) and sin(t) in terms of x and y, then substitute into the identity.

Subtract the coordinates of the initial point from the coordinates of the terminal point: $(x_2 - x_1, y_2 - y_1)$.