Convert the rectangular equation to polar form. (Use theta for 𝜃 as necessary.)x2 + y2 − 6ax = 0
Question
Convert the rectangular equation to polar form.
Use for as necessary.
Given the equation:
Solution
To convert the given rectangular equation x² + y² - 6ax = 0 to polar form, we can follow these steps:
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Recall the relationships between rectangular coordinates (x, y) and polar coordinates (r, θ): x = rcos(θ), y = rsin(θ), and r² = x² + y².
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Substitute x = rcos(θ) and r² = x² + y² into the equation. This gives us r² - 6ar cos(θ) = 0.
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Rearrange the equation to get it in standard polar form. The polar form of the equation is r = 6a cos(θ).
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