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, often denoted as 't'.

Front

How do you convert parametric equations to rectangular form?

Back

To convert parametric equations to rectangular form, eliminate the parameter by expressing one variable in terms of the other.

Front

What is the rectangular equation for the parametric equations x = 4cosθ and y = 3sinθ?

Back

The rectangular equation is \( \frac{y^2}{9} + \frac{x^2}{16} = 1 \), which represents an ellipse.

Front

What shape does the parametric equation x = 3cos(t), y = 3sin(t) represent?

Back

It represents a circle with a radius of 3.

Front

What is the rectangular equation for the parametric equations x = 4 - t and y = 2t + 1?

Back

The rectangular equation is y = 9 - 2x.

Front

What is the general form of a parametric equation for a circle?

Back

The general form is x = r cos(t) and y = r sin(t), where r is the radius.

Front

What is an ellipse in terms of parametric equations?

Back

An ellipse can be represented parametrically as x = a cos(t) and y = b sin(t), where a and b are the semi-major and semi-minor axes.

Front

How do you identify the shape of a graph from parametric equations?

Back

To identify the shape, convert the parametric equations to rectangular form and analyze the resulting equation.

Front

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

Back

The parameter 't' typically represents time or another independent variable that defines the position of points on the curve.

Front

What are the key characteristics of a parametric equation for a line?

Back

A parametric equation for a line can be expressed as x = x0 + at and y = y0 + bt, where (x0, y0) is a point on the line and (a, b) is the direction vector.