Instructions: Fill in the blanks with the appropriate terms related to polar coordinates.
The ____________[1] coordinate system specifies a point using its distance from the origin and the angle it makes with the positive -axis.
In the polar coordinate system, the fixed point at the origin is called the ____________[2].
The ____________[3] is the initial ray from the pole, usually aligned with the positive -axis.
A point in the plane is represented in polar coordinates as ____________[4], where is the directed distance from the pole and is the directed angle.
The polar coordinates and Cartesian coordinates are related as follows: __________________[5] __________________[6] __________________[7] __________________[8]
When converting from Cartesian to polar coordinates, the ____________[9] of the point must be considered to determine the correct angle.
To graph a polar equation, one can calculate values of for different values of ____________[10] and plot the corresponding points.
If substituting with results in an equivalent equation, the graph is symmetric about the line ____________[11].
If substituting with results in an equivalent equation, the graph is symmetric about the ____________[12].
If substituting with results in an equivalent equation, the graph is symmetric about the ____________[13].
A ____________[14] is a family of polar graphs defined by equations such as or , which can form inner loops, dimples, or convex shapes.
A ____________[15] curve is a polar graph with the equation or , where the number of petals depends on .
A ____________[16] is the set of points whose distance from a fixed point (focus) is in a constant ratio to its distance from a fixed line (directrix).
If the eccentricity of a conic is less than 1, the shape is a(n) ____________[17].
If the eccentricity of a conic is exactly 1, the shape is a(n) ____________[18].
If the eccentricity of a conic is greater than 1, the shape is a(n) ____________[19].
The general equation of a conic in polar form is , where represents the ____________[20] and represents the distance between the focus and the directrix.