Find the centre and radius of the circle `x^2+y^2+8x+10y-8=0`.

Determine the centre and the radius if the circle x^2+y^2-8x+10y-12=0

Does each of the following equation represent a circle? If so, find the centre and radius of the circle. (i) x ^2 + y ^2 + 2x + 4y - 45 = 0

Does each of the following equation represent a circle? If so, find the centre and radius of the circle. (iii) 2x ^2 + y ^2 - 6x -8y - 11 = 0

Does each of the following equation represent a circle? If so, find the centre and radius of the circle. (ii) x ^2 + y ^2 - 4x + 5 = 0

Show that the equation x^2+y^2-6x+8y+21=0 represents a circle.Find the centre and radius of the circle.

Find the equation of the circle whose centre is (4, 5) and which passes through the centre of the circle x ^2 + y ^2 + 4x -6y - 12 = 0

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

Find the equation of the diameter of the circle x ^2 + y ^2 - 14x + 6y + 9 = 0 which passes through the point (2, 1).

Find the equations of two tagents to the circle x ^2 + y ^2 = 34 which are parallel to the straight line 5y - 3x + 7 = 0.

Show that x + y = 1 is the equation of the line of a diameter of the circle x ^2 + y ^2 - 4x + 2y + 1 = 0