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Chapter 30: Problem 973

Transform the equation \(\mathrm{xy}=4\) to polar coordinates.

Short Answer

Expert verified
The equation \(xy = 4\) can be transformed to polar coordinates by replacing x and y with their polar coordinate formulas, resulting in the equation \(r^2 \cos(\theta) \sin(\theta) = 4\).

Step by step solution

01

Write the equation in Cartesian coordinates

The given equation is in Cartesian coordinates: \( xy = 4 \)
02

Replace x and y with their polar coordinate formulas

We substitute \(x\) with \(r \cos(\theta)\) and \(y\) with \(r \sin(\theta)\) in the given equation: \( (r \cos(\theta)) (r \sin(\theta)) = 4 \) Now we have an equation with polar coordinates.
03

Simplify the polar coordinates equation

The equation in polar coordinates is: \( r^2 \cos(\theta) \sin(\theta) = 4 \) This is our final equation, transformed from Cartesian coordinates (\(xy = 4\)) to polar coordinates (\(r^2 \cos(\theta) \sin(\theta) = 4\)).

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Most popular questions from this chapter

Transform the equation \(\rho=2 \cos \theta\) to rectangular coordinates.

Convert the equation \(\mathrm{r}=\tan \theta+\cot \theta\) to an equation in cartesian coordinates.

Transform the equation \(x^{2}+y^{2}-x+3 y=3\) to a polar equation.

Draw the graph of \(\rho=2 \cos \theta\).

Transform the equation \(\mathrm{r}=4 /(2-3 \sin \theta)\) to an equation in cartesian coordinates.
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