At any point $$(x, y)$$ on a curve if the length of the subnormal is $$(x-1)$$ and the curve passes through $$(1,2)$$, then the curve is a conic. A vertex of the curve is

A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness, which melts at a rate of 50 cm$$^3$$ /min. When the thickness of the ice is 15 cm, the rate at which the thickness of ice decreases is ........ cm/min.

Find the minimum value of $$2x+3y$$, when $$xy=6$$.

The volume of a spherical balloon is increasing at the rate of $$30 \mathrm{~cm}^3$$ per minute. Find the rate of change of surface area of the balloon, when its radius is $$6 \mathrm{~cm}$$.