Consider the collection of all curve of the form `y = a – bx^(2)` that pass through the point (2, 1), where ‘a’ and ‘b’ are positive constants. Determine the value of ‘a’ and ‘b’ that will minimize the area of the region bounded by` y = a – bx^(2)` and x-axis. Also find the minimum area.

Answer

`b = 1/8, A_("minimum") = 4sqrt(3)` sq.units