Mathematics: Rewrite in rectangular form r=8sin (theta)-2cos (theta)

ok this is hard.Step-by-step explanation:...

Rewrite in rectangular form r=8sin (theta)-2cos

PerfectMagZ

08.01.2022

The equation in rectangular form is:

(x+1)^2+(y-4)^2=17

Step-by-step explanation:

We are given a expression in polar coordinate form as:

$r=8\sin(\theta)-2\cos(\theta)$

We know that:

$x=r\cos\theta\ and\ y=r\sin\theta$

This means that:

$sin\theta=\dfrac{y}{r}\ and cos\theta=\dfrac{x}{r}$

Hence,

$r=\dfrac{8y}{r}-\dfrac{2x}{r}\\\\r^2=8y-2x$

Also, we know that:

x^2+y^2=r^2

Hence,

$x^2+y^2=8y-2x\\\\x^2+2x+y^2-8y=0\\\\(x+1)^2+(y-4)^2=17$

Hence, the following equation is a equation of a circle with center at (-1,4) and radius √17.

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