Find the equation of the diameter of the circle `x^2 + y^2 - 2x + 4y = 0` which passes thorugh the origin.

The equation of one of the diameters of the circle x^2+y^2 - 6x + 2y =0 is:

Find the equations of the tangents to the curve 3x^2 - y^2 = 8 , which pass thorugh the point (4/3,0)

One of the diameters of the circle x^2+y^2-12x+4y+6=0 is given by

Find the equation of the circle which cuts orthogonally the circle x^2 + y^2 – 6x + 4y -3 = 0 ,passes through (3,0) and touches the axis of y.

Find the parametric representation of the circle x^2 + y^2 - 2x + 4y -4=0 .

Find the equation of the circle, whose centre lies on the line 2x- y- 3 = 0 and which passes through the points (3, - 2) and (-2, 0).

Find the equation of the circle concentric with the circle x^2 + y^2+4x+ 6y+11=0 and Passing through the point (5, 4).

Find the equation of the circle concentric with the circle x^(2) + y^(2) - 8x + 6y -5 = 0 and passing through the point (-2, -7).

Find the parametric form of the equation of the circle x^2+y^2+p x+p y=0.

Find the equation of the tangents to the circle x^(2)+y^(2)-2x-4y-4=0 which are (i) parallel (ii) perpendicular to the line 3x-4y-1=0