If $$A = \left[ {\matrix{ {5a} & { - b} \cr 3 & 2 \cr } } \right]$$ and $$A$$ adj $$A=A$$ $${A^T},$$ then $$5a+b$$ is equal to :

The eccentricity of the hyperbola whose length of the latus rectum is equal to $$8$$ and the length of its conjugate axis is equal to half of the distance between its foci, is :

If one of the diameters of the circle, given by the equation, $${x^2} + {y^2} - 4x + 6y - 12 = 0,$$ is a chord of a circle $$S$$, whose centre is at $$(-3, 2)$$, then the radius of $$S$$ is :

Two sides of a rhombus are along the lines, $$x - y + 1 = 0$$ and $$7x - y - 5 = 0$$. If its diagonals intersect at $$(-1, -2)$$, then which one of the following is a vertex of this rhombus?