Parametric Equations

Front

The variable 't' in parametric equations is called a

Back

parameter.

Front

Given the parametric equations x = 1 - 2t and y = 4t + 1, find the point when t = 3.

Back

(-5, 13)

Front

Given the parametric equations x = t² - 2 and y = -t + 2, find the ordered pair when t = -2.

Back

(2, 4)

Front

Write the rectangular equation for the parametric equations x = 4 - t and y = 2t + 1.

Back

y = 9 - 2x.

Front

Convert the parametric equations x = 2t and y = t² + 3 into rectangular form.

Back

y = ¼ x² + 3.

Front

What is a parametric equation?

Back

An equation that expresses a set of quantities as explicit functions of a number of independent variables, known as parameters.

Front

How do you eliminate the parameter in parametric equations?

Back

By expressing one variable in terms of the other and substituting.

Front

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

Back

It represents a variable that can take on different values, allowing the equations to describe a curve or path.

Front

What is the relationship between parametric equations and Cartesian coordinates?

Back

Parametric equations can be converted into Cartesian coordinates to represent the same curve in a different form.

Front

What does it mean for a curve to be defined parametrically?

Back

It means that the coordinates of the points on the curve are expressed as functions of one or more parameters.