Parametric Equations Questions

They allow for more flexible representations of curves.

They are easier to solve analytically.

They require fewer variables.

They are more accurate.

By providing a single equation for both x and y coordinates

By allowing the description of motion in terms of a third variable, usually time

By restricting the motion to linear paths only

By simplifying the calculation of derivatives

Parametric representation uses parameters to define a curve, while rectangular representation uses x and y coordinates.

Parametric representation uses x and y coordinates, while rectangular representation uses parameters.

Both representations use parameters to define a curve.

Both representations use x and y coordinates.

they do not pass the vertical line test.

they are not continuous.

they have no tangent lines.

they are not differentiable.

y = sqrt((x + 4)/3)

y = (x + 4)/3

y = 2x + 1

y = (3x + 4)/2

A circle, with t representing the angle in radians.

An ellipse, with t representing the angle in degrees.

A straight line, with t representing time.

A parabola, with t representing the distance.

dy/dx = $$\frac{2t + 2}{3t^2 - 1}$$ ; Horizontal tangent at t = -1, Vertical tangent at t = $$1/\sqrt{3}$$

dy/dx = $$\frac{(2t + 2)}{(3t^2 - 1)}$$ ; Horizontal tangent at t = 0, Vertical tangent at t = 1

dy/dx = $$\frac{2t + 2}{3t^2 - 1}$$ ; Horizontal tangent at t = 1, Vertical tangent at t = 0

$$\frac{2t + 2}{3t^2 - 1}$$ ; Horizontal tangent at t = 1, Vertical tangent at t = 1

(-5, 13)

(13, -5)

(5, 13)

(13, 5)