Chapter 10: Q.30 (page 699)

In Problems 30 and 31, convert each polar equation to a rectangular equation.
$r = \frac{4}{1 - \cos θ}$

Short Answer

Expert verified

The rectangular equation is $y^{2} = 8 x + 16$

Step by step solution

Step 1. Given Information

Given to convert the below polar equation to a rectangular equation.

$r = \frac{4}{1 - \cos θ}$

Step 2. Calculation

A polar equation is converted to rectangular equation by using the substitutions $r^{2} = x^{2} + y^{2}, r \cos θ = x, r \sin θ = y$

Rewriting the given equation to get the above terms:

$r = \frac{4}{1 - \cos θ} r (1 - \cos θ) = 4 r - r \cos θ = 4 r = 4 + r \cos θ r^{2} = {(4 + r \cos θ)}^{2}$

Plugging the values:

$x^{2} + y^{2} = {(4 + x)}^{2} x^{2} + y^{2} = 16 + 8 x + x^{2} y^{2} = 8 x + 16$

Step 3. Conclusion

The rectangular equation of the given polar equation is $y^{2} = 8 x + 16$

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In Problems 30 and 31, convert each polar equation to a rectangular equation.
$r = \frac{4}{1 - \cos θ}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Conclusion

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In Problems 30 and 31, convert each polar equation to a rectangular equation.r=41-cosθ

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

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In Problems 30 and 31, convert each polar equation to a rectangular equation.
$r = \frac{4}{1 - \cos θ}$