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1.
The equation x^2+y^2-4x+6y-12=0 after translation to the center becomes:
2.
The image of the point (4, 1) in the line y = x - 1 (i.e., x - y - 1 = 0) is:
3.
The locus of a point P such that the tangents from P to the circle x^2+y^2=25 are perpendicular to each other is:
4.
The angle of rotation required to eliminate the xy-term from x^2 + 2*sqrt(3)*xy + 3y^2 = 6 is:
5.
The locus of a point P such that PA^2 + PB^2 = 50, where A = (3, 0) and B = (-3, 0), is:

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