Which conic section has the polar equation r=a sintheta?

1 Answer
Dec 3, 2014

Remember:

{(x=r cos theta),(y=r sin theta):}

and

x^2+y^2=r^2.

By multiplying by r,

r=a sin theta => r^2=a r sin theta

by rewriting in rectangular coordinates,

=>x^2+y^2=ay => x^2+y^2-ay=0

by adding (a/2)^2,

=> x^2+y^2-ay+(a/2)^2=(a/2)^2

by completing the square,

x^2+(y-a/2)^2=(a/2)^2

Hence, it is a circle with radius a/2, centered at (0,a/2).


I hope that this was helpful.