1. **State the problem:** Convert the rectangular equation $$14y = x^2 + y^2$$ to polar form and solve for $$r$$ in terms of $$\theta$$. 2. **Recall the polar-rectangular relationships:** $$x = r\cos\theta$$ $$y = r\sin\theta$$ $$x^2 + y^2 = r^2$$ 3. **Substitute into the given equation:** $$14y = x^2 + y^2 \implies 14(r\sin\theta) = r^2$$ 4. **Rewrite the equation:** $$14r\sin\theta = r^2$$ 5. **Divide both sides by $$r$$ (assuming $$r \neq 0$$):** $$\cancel{r}14\sin\theta = \cancel{r}r \implies 14\sin\theta = r$$ 6. **Final polar form solved for $$r$$:** $$r = 14\sin\theta$$ This means the radius $$r$$ depends on the angle $$\theta$$ as $$14\sin\theta$$.