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

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 equation of the circle concentric with the circle x ^2 + y ^2 - 8x + 12y + 15 = 0 and passing through the point (5, 4).

Find the equation of the circle of radius 5 units which is concentric with the circle x ^2 + y ^2 + 2x - 4y = 0

Find the equation of the circle whose radius 4 and which is concentric with the circle x ^2 + y ^2 + 2x - 6y = 0.

Find the equation of the circle whose centre is (2, 3) and which touches the line 3x - 4y - 1 = 0.

Find the equation of the tanget to the parabola (i) y^2 = 4x which is parllel to 2x + y + 3 = 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

Which of the following equation represent circles? (iv) x ^2 + y ^2 + 4x + 16y + 59 = 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

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