Find the locus of a point such that the sum of the squares of its distances from the axes is $4$.

Tangents are drawn from the point $(17,7)$ to the circle $x^2+y^2=169$.
$STATEMENT-1$: The tangents are mutually perpendicular.
$STATEMENT-2$: The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is $x^2+y^2=338$.

Find the locus of the midpoint of the chord of the circle $x^2 + y^2 = 16$ which is a tangent to the hyperbola $9x^2 - 16y^2 = 144$.

If the locus of the point,whose distances from the point $(2,1)$ and $(1,3)$ are in the ratio $5:4$,is $ax^2+by^2+cxy+dx+ey+170=0$,then the value of $a^2+2b+3c+4d+e$ is equal to:

The locus of the mid-points of the chords of the circle $x^2+y^2=16$ which are tangents to the hyperbola $9x^2-16y^2=144$ is

$A$ cow is tied to a corner (vertex) of a regular hexagonal fenced area of side $a \ m$ by a rope of length $\frac{5a}{2} \ m$ in a grass field. (The cow cannot graze inside the fenced area). What is the maximum possible area of the grass field to which the cow has access to graze?