Question

(X-1)^2 + (y-3)^2=10 convert equation from rectangular form to polar form

Answer 1

Answer:

$r= 2(cos(\theta) + 3sin(\theta))$

Step-by-step explanation:

To convert an equation of rectangular shape to polar form use the following equivalences

$x=rcos(\theta)$

$y=rsin(\theta)$

$x^2 + y^2=r^2$

In this case we have the following equation.

$(x-1)^2 + (y-3)^2=10$

First we expanded the expression

$(x-1)^2 + (y-3)^2=10\\\\(x^2 -2x +1) +(y^2 -6y + 9) = 10\\\\\\x^2 +y^2 -2x -6y = 10-9-1\\\\x^2 +y^2 -2x -6y = 0$

Now we know that $x^2 + y^2=r^2$, $x=rcos(\theta)$ and $y=rsin(\theta)$

So

$r^2 -2rcos(\theta) -6rsin(\theta) = 0\\\\r^2 - 2r(cos(\theta) + 3sin(\theta))=0\\\\r^2 = 2r(cos(\theta) + 3sin(\theta))\\\\r= 2(cos(\theta) + 3sin(\theta))$