When the coordinate axes are rotated about the origin through an angle π4 in the positive direction, the equation ax2 + 2hxy + by2 = c is transformed to 25x2 + 9y2 = 225. Then the value of (a + 2h + b - √c)2 is:

When the origin is shifted to the point (2, b) by a translation of axes, the coordinates of the point (4, 4) change to (6, 8). When the origin is shifted to (a, b) by a translation of axes, if the transformed equation of x2 + 4xy + y2 = 0 becomes X2 + 2HXY + Y2 + 2GX + 2FY + C = 0, then the value of 2H(G + F) is:

The point (4, 1) undergoes the following two successive transformations: (i) Reflection about the line y = x (ii) Translation through a distance of 2 units along the positive x-axis What are the final coordinates of the point?