The locus of the centre of a circle which cuts the circles $x^2 + y^2 + 4x - 6y + 9 = 0$ and $x^2 + y^2 - 4x + 6y + 4 = 0$ orthogonally is

The hypotenuse of a right-angled triangle has its endpoints at the points $(1, 3)$ and $(-4, 1)$. Find the equations of the legs (perpendicular sides) of the triangle.

If $P$ is a variable point such that the sum of the distances from $P$ to the points $A(2,2)$ and $B(2,-2)$ is $4$,then the locus of $P$ represents

The locus of the third vertex of a right-angled triangle,the ends of whose hypotenuse are $(1,2)$ and $(4,5)$,is

The locus of the centroid of the triangle with vertices at $(a \cos \theta, a \sin \theta)$,$(b \sin \theta, -b \cos \theta)$ and $(1, 0)$ is (where $\theta$ is a parameter).

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 $x^2+y^2=338$.