Parametric Equations Practice

Front

What is a parametric equation?

Back

A parametric equation expresses the coordinates of the points of a curve as functions of a variable, typically denoted as 't'. For example, x = f(t) and y = g(t).

Front

How do you convert parametric equations to rectangular form?

Back

To convert parametric equations to rectangular form, eliminate the parameter 't' to express y as a function of x, or vice versa.

Front

Given the parametric equations x = 2t and y = t^2 + 3, what is the rectangular form?

Back

The rectangular form is y = ¼ x^2 + 3.

Front

What is the significance of the parameter 't' in parametric equations?

Back

The parameter 't' represents a variable that traces out the curve as it changes, allowing for the representation of motion or changes over time.

Front

How do you find the ordered pair from parametric equations?

Back

Substitute the value of 't' into the parametric equations to find the corresponding x and y values, forming the ordered pair (x, y).

Front

For the parametric equations x = t^2 - 2 and y = -t + 2, what is the ordered pair when t = -2?

Back

The ordered pair is (2, 4).

Front

What does the range of 't' indicate in parametric equations?

Back

The range of 't' indicates the interval over which the curve is traced, affecting the portion of the curve that is graphed.

Front

What is the result of eliminating the parameter from the equations x(t) = t^2 + 5 and y(t) = t^2 - 4?

Back

The result is a linear relationship between x and y.

Front

How do you determine which part of a curve is graphed from parametric equations?

Back

Analyze the range of 't' to determine which section of the curve is represented, such as the top or bottom half.

Front

What is the ordered pair when t = 0 for the equations x(t) = e^t - e^-t and y(t) = e^t + e^-t?

Back

The ordered pair is (0, 2).