Problem 1
Given polar equation \(r=f(\theta),\) how can one create parametric equations of the same curve?
Problem 1
T/F: When sketching the graph of parametric equations, the \(x\) and \(y\) values are found separately, then plotted together.
Problem 1
What is the difference between degenerate and nondegenerate conics?
Problem 2
T/F: When plotting a point with polar coordinate \(P(r, \theta), r\) must be positive.
Problem 2
Use your own words to explain what the eccentricity of an ellipse measures.
Problem 3
An equation written as \(y=f(x)\) is written in __________form.
Problem 3
T/F: Every point in the Cartesian plane can be represented by a polar coordinate.
Problem 3
What has the largest eccentricity: an ellipse or a hyperbola?
Problem 3
Find: (a) \(\frac{d y}{d x}\) (b) the equation of the tangent and normal lines to the curve at the indicated \(\theta\) -value. \(r=1 ; \quad \theta=\pi / 4\)
Problem 4
T/F: Every point in the Cartesian plane can be represented uniquely by a polar coordinate.
