Let S be the set of all the natural numbers, for which the line $${x \over a} + {y \over b} = 2$$ is a tangent to the curve $${\left( {{x \over a}} \right)^n} + {\left( {{y \over b}} \right)^n} = 2$$ at the point (a, b), ab $$\ne$$ 0. Then :

The area bounded by the curve y = |x² $$-$$ 9| and the line y = 3 is :

Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle. Then the area of $$\Delta$$PQR is :

Let C be a circle passing through the points A(2, $$-$$1) and B(3, 4). The line segment AB s not a diameter of C. If r is the radius of C and its centre lies on the circle $${(x - 5)^2} + {(y - 1)^2} = {{13} \over 2}$$, then r² is equal to :