Find the general equation of a circle with centre (-3, -4) and radius 3 units.

Determine whether x + y − 1 = 0 is the equation of a diameter of the circle x² + y² − 6x + 4y + c = 0 for all possible values of c .

Find the general equation of the circle whose diameter is the line segment joining the points (−4, −2)and (1, 1) is x²+y²+5x+3y+6=0

Examine the position of the point (2, 3) with respect to the circle x² + y² − 6x − 8y + 12 = 0.

The line 3x+4y−12 = 0 meets the coordinate axes at A and B. Find the equation of the circle drawn on AB as diameter.