Math Problem Statement
Solution
To convert the given polar equation into rectangular coordinates (), we will use the relationships between polar and rectangular coordinates:
Step-by-Step Conversion:
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Start with the polar equation:
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Multiply through by to eliminate the denominator:
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Expand:
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Substitute :
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Solve for :
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Substitute :
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Expand :
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Simplify by canceling from both sides:
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Rearrange to get the general form:
Final Answer:
The rectangular form of the equation is:
Would you like a more detailed explanation of any step or have questions?
Here are 5 related questions for further exploration:
- How do we convert other polar equations, such as , to rectangular form?
- What type of conic section does this rectangular equation represent?
- Can the equation be rewritten in standard form for a parabola?
- How would the equation change if was replaced with ?
- How do the transformations and work geometrically?
Tip: Always check if the final rectangular equation corresponds to a familiar geometric shape (circle, parabola, ellipse, or hyperbola) for a better understanding of the problem!
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Math Problem Analysis
Mathematical Concepts
Polar Coordinates
Rectangular Coordinates
Converting Coordinate Systems
Equations of Conic Sections
Formulas
x = r * cos(θ)
y = r * sin(θ)
r^2 = x^2 + y^2
cos(θ) = x / r
Theorems
Relationship between Polar and Rectangular Coordinates
Suitable Grade Level
Grades 10-12
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