One of the diameters of the circle circumscribing the rectangle $$ABCD$$ is $$4y = x + 7$$. If $$A$$ and $$B$$ are the points $$(-3, 4)$$ and $$(5, 4)$$ respectively, then find the area of rectangle.

Two sides of rhombus $$ABCD$$ are parallel to the lines $$y = x + 2$$ and $$y = 7x + 3$$. If the diagonals of the rhombus intersect at the point $$(1, 2)$$ and the vertex $$A$$ is on the $$y$$-axis, find possible co-ordinates of $$A$$.

From the origin chords are drawn to the circle $${(x - 1)^2} + {y^2} = 1$$. The equation of the locus of the mid-points of these chords is.............

No tangent can be drawn from the point (5/2, 1) to the circumcircle of the triangle with vertices $$\left( {1,\sqrt 3 } \right)\,\,\left( {1, - \sqrt 3 } \right),\,\,\left( {3,\sqrt 3 } \right)$$.