Parametric Equations

Front

What is a parametric equation?

Back

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

Front

What does the variable 't' represent in parametric equations?

Back

The variable 't' is called a parameter.

Front

What is the general form of a parametric equation?

Back

A parametric equation typically has the form x(t) and y(t), where 't' is the parameter.

Front

How do you determine the direction of motion in parametric equations?

Back

The direction of motion is determined by the increasing or decreasing values of the parameter 't'.

Front

What type of curve is formed by the parametric equations x(t) = a cos(t) and y(t) = b sin(t)?

Back

These equations form an ellipse.

Front

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

Back

The range of 't' determines the portion of the curve that is graphed.

Front

How do you find the Cartesian equation from parametric equations?

Back

To find the Cartesian equation, eliminate the parameter 't' from the equations x(t) and y(t).

Front

What is the effect of changing the coefficients in parametric equations?

Back

Changing the coefficients affects the size and shape of the graph.

Front

What is the relationship between parametric equations and calculus?

Back

Parametric equations can be differentiated to find slopes and areas under curves.

Front

How do you graph parametric equations?

Back

To graph parametric equations, plot points for various values of 't' and connect them in the order of 't'.