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Chapter 9: Q. 28 (page 772)

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22鈥�31.
$r = \frac{3}{1 + \cos 胃}$

Short Answer

Expert verified

The equation is $y^{2} = 9 - 6 x .$

Step by step solution

01

Step 1. Given information.

The give equation is $r = \frac{3}{1 + \cos 胃} .$

02

Step 2. Conversion.

Converting the polar co-ordinates into cartesian co-ordinates,

$r = \frac{3}{1 + \cos 胃} r (1 + \cos 胃) = 3 r + r \cos 胃 = 3 \sqrt{x^{2} + y^{2}} + r 路 \frac{x}{r} = 3 [since r = \sqrt{x^{2} + y^{2}} and r \cos 胃 = x] \sqrt{x^{2} + y^{2}} + x = 3$

03

Step 3. Final answer.

On simplifying the equation,

$\sqrt{x^{2} + y^{2}} + x - x = 3 - x \sqrt{x^{2} + y^{2}} = 3 - x {(\sqrt{x^{2} + y^{2}})}^{2} = (3 - x)^{2} x^{2} + y^{2} = 9 + x^{2} - 6 x x^{2} + y^{2} - x^{2} = 9 + x^{2} - 6 x - x^{2} y^{2} = 9 - 6 x$

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Most popular questions from this chapter

In Exercises 48鈥�55 convert the equations given in rectangular coordinates to equations in polar coordinates.

$y = x$

In Exercises 48鈥�55 convert the equations given in rectangular coordinates to equations in polar coordinates.

$x = 0$

Use polar coordinates to graph the conics in Exercises 44鈥�51.

$r = \frac{2}{1 + 3 \cos 胃}$

In Exercises 48鈥�55 convert the equations given in rectangular coordinates to equations in polar coordinates.

$y = x + 1$

In Exercises 32鈥�47 convert the equations given in polar coordinates to rectangular coordinates.

$r = 胃$

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