Polar Coordinates

1. The ____________^[1] coordinate system specifies a point using its distance from the origin and the angle it makes with the positive -axis.

2. In the polar coordinate system, the fixed point at the origin is called the ____________^[2].

3. The ____________^[3] is the initial ray from the pole, usually aligned with the positive -axis.

4. 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.

5. The polar coordinates and Cartesian coordinates are related as follows:
   __________________^[5]
   __________________^[6]
   __________________^[7]
   __________________^[8]

6. When converting from Cartesian to polar coordinates, the ____________^[9] of the point must be considered to determine the correct angle.

7. To graph a polar equation, one can calculate values of for different values of ____________^[10] and plot the corresponding points.

8. If substituting with results in an equivalent equation, the graph is symmetric about the line ____________^[11].

9. If substituting with results in an equivalent equation, the graph is symmetric about the ____________^[12].

10. If substituting with results in an equivalent equation, the graph is symmetric about the ____________^[13].

11. A ____________^[14] is a family of polar graphs defined by equations such as or , which can form inner loops, dimples, or convex shapes.

12. A ____________^[15] curve is a polar graph with the equation or , where the number of petals depends on .

13. 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).

14. If the eccentricity of a conic is less than 1, the shape is a(n) ____________^[17].

15. If the eccentricity of a conic is exactly 1, the shape is a(n) ____________^[18].

16. If the eccentricity of a conic is greater than 1, the shape is a(n) ____________^[19].

17. The general equation of a conic in polar form is
    , where represents the ____________^[20] and represents the distance between the focus and the directrix.