# 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. %Graph the region being described by the inequality.

*y*≥ 5*x*+*y*≤ 3*x*^{2}+*y*^{2}< 100

### Example 3

- Translate each equation into rectangular coordinates.

- rcosθ + r
^{2}sin^{2}θ = 4rsinθ - (hint: multiply through by
*r*) - r = 4 (hint: square both sides.)

### Example 4

- Translate each inequality into rectangular coordinates. Assume
*r*is non-negative.%Graph the region being described by the inequality.

- sin θ < 1/r
- rcos
^{2}θ + rsin^{2}θ = 1 - 5r
^{2}cos^{2}θ + 10rcosθ + 5 -4r^{2}sin^{2}θ + 16rsinθ-16 = 20

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