Calculus II

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The equation in the polar form is `r = 3*cos theta + 4*sin theta`

Converting from Polar to Cartesian form involves using the relations `r^2 = x^2 + y^2` , `x = r*cos theta` and `y = r*sin theta`

`r = 3*cos theta + 4*sin theta`

=>` r = 3*(x/r)+ 4*(y/r)`

=>` r^2 = 3x + 4y`

=> `x^2 + y^2 = 3x + 4y`

=> `x^2 - 3x + y^2 - 4y = 0`

=> `x^2 - 3x + 9/4 + y^2 - 4y + 4 = 4 + 9/4`

=> `(x - 3/2)^2 + (y - 2)^2 = 25/4`

=> `(x - 3/2)^2 + (y - 2)^2 = (5/2)^2`

This is the equation of a circle with center `(3/2, 2)` and radius `5/2`

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