The sides of a rectangle are given by the equations $$x=-2, x=4, y=-2$$ and $$y=5$$

Then the equation of the circle, whose centre is the point of intersection of the diagonals, lying within the rectangle and touching only two opposite sides, is

Two tangents to the circle $$x^2+y^2=4$$ at the points $$\mathrm{A}$$ and $$\mathrm{B}$$ meet at the point $$\mathrm{P}(-4,0)$$. Then the area of the quadrilateral $$\mathrm{PAOB}, \mathrm{O}$$ being the origin, is

The equation of circle with centre at $$(2,-3)$$ and the circumference $$10 \pi$$ units is

The equation of the circle whose centre lies on the line $$x-4 y=1$$ and which passes through the points $$(3,7)$$ and $$(5,5)$$ is