Question

Which rectangular equation is equivalent to the polar equation r csc theta=8?

Answer 1

X^2+(Y-4)^2=16

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Answer 2

X=rcos(t), y=rsin(t). so y/sin(t) = r => csc(t) = r/y. so for now we have r*(r/y)=8. To solve for r, do x^2 + y^2 = r^2, so r=sqrt(x^2 + y^2). So we have sqrt(x^2 + y^2)*(sqrt(x^2 + y^2)/y)=8, or (x^2+y^2)/y = 8, or x^2/y + y = 8.