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'. For example, x(t) and y(t) define the curve in terms of 't'.

Front

Sketch the curve defined by the parametric equations x(t) = 2t + 1 and y(t) = t^2 + 2.

Back

The curve is a parabola that opens upwards, with its vertex shifted to the right due to the linear term in x(t).

Front

Calculate the coordinates for the parametric equations x = 4sin(θ) and y = 2cos(θ) when θ = π/4.

Back

The coordinates are (2√2, √2).

Front

What type of graph is produced by the parametric equations x(t) = t^2 + 5 and y(t) = t^2 - 4?

Back

The graph is linear, as both equations are quadratic in 't' and produce a straight line when plotted against each other.

Front

Find the coordinates for the parametric equations x = t ln(t) and y = ln(t) when t = e.

Back

The coordinates are (e, 1).

Front

Identify the set of parametric equations that satisfies the given data table: x(t) = t^3 - 1, y(t) = t + 2.

Back

This set of equations correctly represents the data table.

Front

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

Back

The variable 't' is a parameter that allows the representation of curves in a two-dimensional space, enabling the tracing of the curve as 't' varies.

Front

Define the term 'coordinate' in the context of parametric equations.

Back

A coordinate is a pair of values (x, y) that represent a point in a two-dimensional space, derived from the parametric equations.

Front

What is the relationship between parametric equations and Cartesian coordinates?

Back

Parametric equations can be converted to Cartesian coordinates by eliminating the parameter 't', resulting in a single equation relating x and y.

Front

Explain how to graph parametric equations.

Back

To graph parametric equations, calculate points for various values of 't', plot these points on the Cartesian plane, and connect them to visualize the curve.