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# Translating Equations and Inequalities between Coordinate Systems Exercises

### Example 1

• Translate each equation into polar coordinates.
1. (x + 2)2 + (y + 2)2 = 4
2. x + y2 = 0
3. (x + y)2 = 4

### Example 2

• Translate each inequality into polar coordinates.
1. y ≥ 5
2. x + y ≤ 3
3. x2 + y2 < 100

### Example 3

• Translate each equation into rectangular coordinates.
1. r cos θ + r2 sin2 θ = 4r sin θ
2. r = 4

### Example 4

• Translate each inequality into rectangular coordinates. Assume r is non-negative.
1. r cos2 θ + r sin2 θ = 1
2. 5r2 cos2 θ + 10r cos θ + 5 – 4r2 sin2 θ + 16r sin θ – 16 = 20
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