If $P = (1, 0)$,$Q = (-1, 0)$,and $R = (2, 0)$ are three given points,then the locus of a point $S$ satisfying the relation $SQ^2 + SR^2 = 2SP^2$ is

The locus of the midpoint of the chord of contact of tangents drawn from a point on the line $4x - 5y = 20$ to the circle $x^2 + y^2 = 9$ is:

Let $ABCD$ be a square. An arc of a circle with $A$ as center and $AB$ as radius is drawn inside the square joining the points $B$ and $D$. Points $P$ on $AB$,$S$ on $AD$,$Q$ and $R$ on $\operatorname{arc} BD$ are taken such that $PQRS$ is a square. Further suppose that $PQ$ and $RS$ are parallel to $AC$. Then,$\frac{\text{Area}(PQRS)}{\text{Area}(ABCD)}$ is

From a point $A(1, 0)$ on the circle $x^2+y^2-2x+2y+1=0$,a chord $AB$ is drawn and it is extended to a point $P$ such that $AP=3AB$. The equation of the locus of $P$ is

The locus of a point which is at a distance of $4$ units from $(3, -2)$ in the $xy$-plane is

If a chord is drawn from the origin to the circle $(x - 1)^2 + y^2 = 1$,then the equation of the locus of the midpoint of this chord is: