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

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Answer 1 · 2014-12-03T03:42:36

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 $(a/2)^2$ ,

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

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

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

I hope that this was helpful.

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