How do you find a polar equation that has the same graph as the equation in x and y, for the following equation?  (x+2)^2 + (y-3)^2 = 13The more steps & explanation you can provide the better,...

How do you find a polar equation that has the same graph as the equation in x and y, for the following equation?  (x+2)^2 + (y-3)^2 = 13

The more steps & explanation you can provide the better, thanks.

Asked on by kboy217

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

Find the polar equation for `(x+2)^2+(y-3)^2=13` :

We replace x with `rcostheta` and y with `rsintheta` :

`(rcostheta+2)^2+(rsintheta-3)^2=13` Expand:

`r^2cos^2theta+4rcostheta+4+r^2sin^2theta-6rsintheta+9=13`

Collect like terms:

`r^2(cos^2theta+sin^2theta)+2r(2costheta-3sintheta)=0`

Use thePythagorean identity:

`r^2=-2r(2costheta-3sintheta)`

`r=-2(2costheta-3sintheta)`

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The polar form is `r=-2(2costheta-3sintheta)`

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This is a circle centered at (-2,3) with radius `sqrt(13)`

Sources:

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