Find the equation of a circle whose diameters are 2x - 3y + 12 = 0 and x + 4y - 5 = 0 and area is 154 square units.

Find the equation of the parabola whose focus is (-3, 2) and the directrix is x + y = 4.

Find the locus of a point which moves in such a way that the square of its distance from the point (3, -2) is numerically equal to its distance from the line 5x - 12y = 13

A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16, find its locus.

Find the separate equations of the pair of lines given by 3x² + 7xy + 2y² + 5x + 5y + 2 = 0.