Question

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

Answer 1

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

Answer 2

covert to rectangular coordinates to get \[x^2+y^2=ax+by\]

Answer 3

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

Answer 4

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

Answer 5

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