The equation $$\sin x(\sin x + \cos x) = k$$ has real solutions, where k is a real number. Then,

The order of the differential equation of all parabolas whose axis of symmetry along X-axis is

The area enclosed by $$y = \sqrt {5 - {x^2}} $$ and $$y = |x - 1|$$ is

Let S be the set of points, whose abscissae and ordinates are natural numbers. Let P $$ \in $$ S, such that the sum of the distance of P from (8, 0) and (0, 12) is minimum among all elements in S. Then, the number of such points P and S is