Expert answers to "The equivalent polar equation for the given rectangular-coordinate..."

College
Algebra
Linear algebra
Alternate coordinate systems

allhvasstH

Answered question

2020-12-24

The equivalent polar equation for the given rectangular-coordinate equation:

x^{2} + y^{2} + 8 x = 0

Answer & Explanation

Asma Vang

Skilled2020-12-25Added 93 answers

Conversion formula for coordinate systems are given as:
a) From polar to rectangular:
$x = r \cos θ$
$y = r \sin θ$
b) From rectangular to polar:
$r = \pm \sqrt{x^{2} + y^{2}}$
$\cos θ = \frac{x}{r}, \sin θ = \frac{y}{r}, \tan θ = \frac{x}{y}$
Converting into equivalent polar coordinates:
$[x^{2} + y^{2} + 8 x = 0$
Put $x = r \cos θ, y = r \sin θ,$
$\Rightarrow {(r \cos θ)}^{2} + {(r \sin θ)}^{2} + 8 r \cos θ = 0$
$\Rightarrow r^{2} \cos^{2} θ + r^{2} \sin^{2} θ + 8 r \cos θ = 0$
$\Rightarrow r^{2} (\cos^{2} θ + \sin^{2} θ) + 8 r \cos θ = 0$
${\cos^{2} θ + \sin^{2} θ = 0}$
$\Rightarrow r^{2} + 8 r \cos θ = 0$
$\Rightarrow r + 8 \cos θ = 0$
Hence, desired equivalent polar coordinates would be $r + 8 \cos θ = 0$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Linear algebra

Didn't find what you were looking for?