From a point $A(0,3)$ on the circle $(x+2)^2+(y-3)^2=4$,a chord $AB$ is drawn and it is extended to a point $Q$ such that $AQ=2AB$. Then the locus of $Q$ is

$A$ point $P(x, y)$ moves such that the sum of the squares of its distances from the points $(1, 2)$ and $(-2, 1)$ is $14$. Let $f(x, y) = 0$ be the locus of $P$,which intersects the $x$-axis at points $A, B$ and the $y$-axis at points $C, D$. Then the area of the quadrilateral $ACBD$ is equal to:

The equation of the locus of a point which moves so as to be at equal distances from the point $(a, 0)$ and the $y$-axis is

If $P(1, 0)$,$Q(-1, 0)$,and $R(2, 0)$ are three given points,then find the locus of $S(x, y)$ which satisfies the relation $SQ^2 + SR^2 = 2SP^2$.

$A$ circle touches both the $y$-axis and the line $x+y=0$. Then the locus of its center is

If the sum of the distances from a variable point $P$ to the given points $A(1,0)$ and $B(0,1)$ is $2$,then the locus of $P$ is