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## anonymous 5 years ago show that the graph of r = a cos θ + b sin θ is a circle, and find its center and radius

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1. anonymous

multiply through by r to get $r^2=ar\cos\theta +br\sin\theta$

2. anonymous

covert to rectangular coordinates to get $x^2+y^2=ax+by$

3. anonymous

now get into the standard form for a circle by completing the square

4. anonymous

i.e. $(x-\frac{a}{2})^2+(y-\frac{b}{2})^2=\frac{a^2+b^2}{4}$

5. anonymous

so your center is $(\frac{a}{2},\frac{b}{2})$ and the radius is $\frac{a+b}{2}$

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