$A$ point moves in such a way that the sum of the squares of its distances from the points $A(2, 0)$ and $B(-2, 0)$ is always equal to the square of the distance between $A$ and $B$. The locus of the point is

The locus of the point of intersection of the tangents to the circle $x^2+y^2=a^2$ which make complementary angles with the $X$-axis is

The centres of a set of circles,each of radius $3$,lie on the circle ${x^2} + {y^2} = 25$. The locus of any point in the set is

If $A=(1,2), B=(2,1)$ and $P$ is a variable point satisfying the condition $|PA-PB|=3$,then the locus of $P$ is

$A$ variable circle is drawn passing through the origin $O$. It intersects the $X$ and $Y$ axes at points $A$ and $B$ respectively,such that $OA + 2OB = K$ (a non-zero constant). The circle always passes through a fixed point $P$ other than the origin. The point $P$ lies on -

Let $\Gamma$ be a circle with diameter $AB$ and centre $O$. Let $l$ be the tangent to $\Gamma$ at $B$. For each point $M$ on $\Gamma$ different from $A$,consider the tangent $t$ at $M$ and let it intersect $l$ at $P$. Draw a line parallel to $AB$ through $P$ intersecting $OM$ at $Q$. The locus of $Q$ as $M$ varies over $\Gamma$ is