Multiple Choice
In the polar coordinate system, what is the name for a set of coordinates such as the one indicated with (for example, )?
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9. Polar Equations
Polar Coordinate System
Multiple Choice
Given the polar equation , which of the following is its equivalent Cartesian equation?
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Verified step by step guidance1
Recall the relationships between polar and Cartesian coordinates: \(r = \sqrt{x^{2} + y^{2}}\), \(x = r \cos(\theta)\), and \(y = r \sin(\theta)\).
Start with the given polar equation: \(r = 9 \cos(\theta)\).
Substitute \(\cos(\theta)\) with its Cartesian equivalent \(\frac{x}{r}\), so the equation becomes \(r = 9 \cdot \frac{x}{r}\).
Multiply both sides of the equation by \(r\) to eliminate the denominator: \(r^{2} = 9x\).
Replace \(r^{2}\) with \(x^{2} + y^{2}\) to get the Cartesian form: \(x^{2} + y^{2} = 9x\).
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