Equation of a circle passing through origin is `x^(2) + y^(2) - 6x + 2 y = 0`. What is the equation of one of its diameter ?

The equation of diameter of a circle passing through origin is x+y=1 and the greatest distance of any point of the circle from the diameter is sqrt(5) , then an equation of the circle is: (A) x^2+y^2-2x+4y=0 (B) x^2+y^2-4x+2y=0 (C) x^2+y^2+2x-2y=0 (D) none of these

Find the equation of circle passing through the origin and cutting the circles x^(2) + y^(2) -4x + 6y + 10 =0 and x^(2) + y^(2) + 12y + 6 =0 orthogonally.

Find the equation of circle passing through the origin and cutting the circles x^(2) + y^(2) -4x + 6y + 10 =0 and x^(2) + y^(2) + 12y + 6 =0 orthogonally.

(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.

Find the equation of the circle passing through the origin, having its centre on the line x + y = 4 and intersecting the circle x^2 + y^2 - 4x + 2y + 4 = 0 orthogonlly.

Equation of that diameter of circle x^(2) + y^(2) - 6x + 2y - 8 = 0 , which passes through origian , is

Find the equation of the circle passing through the point of intersection of the circles x^2 + y^2 - 6x + 2y + 4 = 0, x^2 + y^2 + 2x - 4y -6 = 0 and with its centre on the line y = x.