The maximum possible value of $x^2+y^2-4x-6y$,where $x, y$ are real,subject to the condition $|x+y|+|x-y|=4$ is

The locus of a point which moves in such a way that its distance from $(0,0)$ is three times its distance from the $x$-axis is given by:

If $A(\cos \alpha, \sin \alpha)$,$B(\sin \alpha, -\cos \alpha)$,and $C(1, 2)$ are the vertices of a $\Delta ABC$,then as $\alpha$ varies,the locus of its centroid is

The number of pairs $(a, b)$ of positive real numbers satisfying $a^4+b^4 < 1$ and $a^2+b^2 > 1$ is

The locus of the middle points of chords of the circle $x^2 + y^2 - 2x - 6y - 10 = 0$ which pass through the origin is:

$A$ point moves such that the square of its distance from the point $(3, -2)$ is numerically equal to its distance from the line $5x - 12y = 13$. The equation of the locus of the point is