Understanding Parametric Equations of Conic Sections

What identity is used as the basis for defining the unit circle in parametric equations?

• Euler's identity

• Pythagorean identity

• Trigonometric identity

• Algebraic identity

When using the parametric representation x = sine(t) and y = cosine(t), where does the unit circle start?

• On the negative y-axis

• On the negative x-axis

• On the positive y-axis

• On the positive x-axis

How does the unit circle move when x = cosine(t) and y = sine(t) in parametric form?

• Horizontally

• Clockwise

• Counterclockwise

• Vertically

In Desmos, what is the purpose of using a slider for parametric equations?

• To switch between different graphs

• To adjust the size of the graph

• To change the color of the graph

• To visualize the direction and movement

What is the center of the ellipse defined by the parametric equations x = 5cos(t) + 3 and y = 3sin(t) - 4?

• (0, 0)

• (-3, 4)

• (5, 3)

• (3, -4)

Which identity is used to define a hyperbola in parametric form?

• Sine squared plus cosine squared

• Cosine squared minus sine squared

• Secant squared minus tangent squared

• Tangent squared plus secant squared

In the parametric representation of a hyperbola, which function is associated with the positive quantity?

• Cosine

• Secant

• Tangent

• Sine

Why are parabolas considered less exciting in terms of parametric representation?

• They involve complex trigonometric functions

• They do not involve trigonometric functions

• They require multiple variables

• They are not conic sections

What is the parametric representation of a parabola if y = x^2?

• x = cos(t), y = sin(t)

• x = t^2, y = t

• x = t, y = t^2

• x = sin(t), y = cos(t)

Which conic section's parametric representation does not rely on trigonometric identities?

• Circle

• Ellipse

• Hyperbola

• Parabola