The area enclosed within the curve $$\left| x \right| + \left| y \right| = 1$$ is .................

Let A be the centre of the circle $${x^2}\, + \,{y^2}\, - \,2x\,\, - 4y\, - 20 = 0\,$$. Suppose that the tangents at the points B (1, 7) and D (4. - 2) on the circle meet at the point C. Find the area of the quadrilateral ABCD.

Find the equations of the circle passing through (- 4, 3) and touching the lines x + y = 2 and x - y = 2.

The equation $${{{x^2}} \over {1 - r}} - {{{y^2}} \over {1 + r}} = 1,\,\,\,\,r > 1$$ represents