# Translating Equations and Inequalities between Coordinate Systems Exercises

### Example 1

- Translate each equation into polar coordinates.

- (
*x*+ 2)^{2}+ (*y*+ 2)^{2}= 4 *x*+*y*^{2}= 0- (
*x*+*y*)^{2}= 4

### Example 2

- Translate each inequality into polar coordinates.

*y*≥ 5*x*+*y*≤ 3*x*^{2}+*y*^{2}< 100

### Example 3

- Translate each equation into rectangular coordinates.

*r*cos*θ*+*r*^{2}sin^{2}*θ*= 4*r*sin*θ**r*= 4

### Example 4

- Translate each inequality into rectangular coordinates. Assume
*r*is non-negative.

*r*cos^{2}*θ*+*r*sin^{2}*θ*= 1- 5
*r*^{2 }cos^{2 }*θ*+ 10*r*cos*θ*+ 5 – 4*r*^{2 }sin^{2 }*θ*+ 16*r*sin*θ*– 16 = 20