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Find a cartesian equation for the curve. r = 10 sin(θ) + 10 cos(θ)

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Explanation:

Multiply both sides by


{r}^(2) = 10r \sin( \alpha ) + 10r \cos( \alpha )

Recall that


{r}^(2) = {x}^(2) + {y}^(2)


x = r \cos( \alpha )


y = r \sin( \alpha )

So we have


{x}^(2) + {y}^(2) = 10y + 10x


{x}^(2) - 10x + {y}^(2) - 10y = 0

Complete the square for both equations and we will get


{x}^(2) - 10x + 25 + {y}^(2) - 10y + 25 = 50


(x - 5) {}^(2) + (y - 5) {}^(2) = 50

This is a circle with a center (5,5) and a radius of 5 times root 2.

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