Circle ` x^(2) + y^(2) - 8x + 4y + 4 = 0 ` touches

If the circle x^(2) + y^(2) + 8x - 4y + c = 0 touches the circle x^(2) + y^(2) + 2x + 4y - 11 = 0 externally and cuts the circle x^(2) + y^(2) - 6x + 8y + k = 0 orthogonally then k =

Statement I The circle x^(2) + y^(2) - 6x - 4y - 7 = 0 touches y-axis Statement II The circle x^(2) + y^(2) + 6x + 4y - 7 = 0 touches x-axis Which of the following is a correct statement ?

The circle x^2 + y^2 - 8x + 4y + 4 = 0 toches

If the circumference of the circle x^(2) + y^(2) + 8x + 8y - b = 0 is bisected by the circle x^(2) + y^(2) - 2x + 4y + a = 0 , then a + b =

The centres of those circles which touch the circle x^(2) + y^(2) - 8x - 8 y - 4 = 0 externally and also touch the x - axis, lie on

The centres of those circles which touch the circle x^(2) + y^(2) - 8x - 8 y - 4 = 0 externally and also touch the x - axis, lie on

(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.

Show that the circles x^(2) + y^(2) - 8x - 4y - 16 = 0 and x^(2) + y^(2) - 2x + 4y + 4 = 0 touch each other internally and find the coordinates of their point of contact.