Eccentricities and Directrices
Exercises 29–36 give the eccentricities of conic sections with one focus at the origin along with the directrix corresponding to that focus. Find a polar equation for each conic section.
e = 2, x = 4
Tangent Lines to Parametrized Curves
In Exercises 1−14, find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of d²y/dx² at this point.
x = t + eᵗ, y = 1 − eᵗ, t = 0
Examples of Polar Equations
[Technology Exercise] Graph the lines and conic sections in Exercises 65–74.
r = −2 cos θ
Cartesian to Polar Equations
Replace the Cartesian equations in Exercises 53–66 with equivalent polar equations.
x - y = 3
Polar to Cartesian Equations
Replace the polar equations in Exercises 27–52 with equivalent Cartesian equations. Then describe or identify the graph.
r² = 4r sin θ
Graphing Sets of Polar Coordinate Points
Graph the sets of points whose polar coordinates satisfy the equations and inequalities in Exercises 11–26.
θ = π/2, r ≥ 0
