Get the answer to "To find: The equivalent polar equation for the..."

College
Algebra
Linear algebra
Alternate coordinate systems

Kyran Hudson

Answered question

2021-02-08

To find: The equivalent polar equation for the given rectangular-coordinate equation.
Given:
$x^{2} + y^{2} + 8 x = 0$

Answer & Explanation

faldduE

Skilled2021-02-09Added 109 answers

Concept used: 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:
$r = \pm \sqrt{x^{2} + y^{2}}$
$\cos θ = \frac{x}{r}; \sin θ = \frac{y}{r}; \tan θ = \frac{x}{y}$
Calculation:
Converting into equivalent polar equation
$x^{2} + y^{2} + 8 x = 0$
Put ${x} = {r} \cos {θ}, {y} = {r} \sin {θ},$
$x = r \cos θ, y = r \sin θ$
$\Rightarrow {(r \cos θ)}^{2} + {(r \sin θ)}^{2} + 8 r \cos θ = 0$
$\Rightarrow r^{2} \cos^{2} θ + r^{2} \sin^{2} θ + 8 r \cos θ = 0$
$\Rightarrow r^{2} (\cos^{2} θ + \sin^{2} θ) + 8 r \cos θ = 0 {\cos^{2} θ + \sin^{2} θ = 1}$
$\Rightarrow r^{2} + 8 r \cos θ = 0$
$\Rightarrow r + 8 \cos θ = 0$
Thus, desired equivalent polar equation 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?