The circle `x^2+y^2 - 4x-8y + 16 = 0` rolls up the tangent to it at `(2+sqrt3, 3)` by `2` units,assuming the x-axis as horizontal, find the equation of the circle in the new position.

The circle x^2 + y^2 - 4x - 8y + 16 = 0 rolls up along the tangent to it at (2 + sqrt3, 3) by 2 units. Assuming the x-axis as horizontal, find the equation of the circle in the new position.

If the circle x^(2) + y^(2) -4x - 8y + 16 =0 rolls up the tangent to it at (2 + sqrt(3), 3) by 2 units (assumes x-axis as horizontal), then the centre of the circle in the new position is

If the circle x^(2) + y^(2) -4x - 8y + 16 =0 rolls up the tangent to it at (2 + sqrt(3), 3) by 2 units (assumes x-axis as horizontal), then the centre of the circle in the new position is

Find the equation of a tangent to the circle x^2+y^2-3x+2y=0 at origin.

The circle (x-a)^2 + (y-a)^2 = a^2 is rolled on the y-axis in the positive direction through one complete revolution. Find the equation of the circle in its new position.

The circle (x-a)^2+(y-a)^2=a^2 is rolled on the y-axis in the positive direction through one complete revolution. Find the equation of the circle in its new-position.

A circle touches y-axis at (0, 2) and has an intercept of 4 units on the positive side of x-axis. The equation of the circle, is

A circle touches y-axis at (0, 2) and has an intercept of 4 units on the positive side of x-axis. The equation of the circle, is

(i) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 6x + 12y + 15 = 0 and of double its radius. (ii) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 2x - 4y + 1 = 0 and whose radius is 5. (iii) Find the equation of the cricle concentric with x^(2) + y^(2) - 4x - 6y - 3 = 0 and which touches the y-axis. (iv) find the equation of a circle passing through the centre of the circle x^(2) + y^(2) + 8x + 10y - 7 = 0 and concentric with the circle 2x^(2) + 2y^(2) - 8x - 12y - 9 = 0 . (v) Find the equation of the circle concentric with the circle x^(2) + y^(2) + 4x - 8y - 6 = 0 and having radius double of its radius.

Area of the triangle formed by the positive x-axis and the normal and tangent to the circle x^2+y^2=4 at the point is (1,sqrt3) is