$A(2,3)$ and $B(3,-5)$ are two vertices of $\triangle ABC$. If the centroid of the $\triangle ABC$ moves on the line $2x+y-2=0$,then the locus of $C$ is

If $a, b, c$ are in harmonical progression,then the line $bcx + cay + ab = 0$ passes through a fixed point whose coordinates are:

In $\triangle ABC$,if $A$ is $(1,2)$,and $B$ and $C$ lie on the line $y=x+\alpha$ (where $\alpha$ is a variable),then the locus of the orthocenter of the triangle is:

Two particles $A$ and $B$ move from rest along a straight line with constant accelerations $f$ and $h,$ respectively. If $A$ takes $m$ seconds more than $B$ and describes $n$ units more than that of $B$ to acquire the same speed, then

$AB$ is a line segment moving between the axes such that '$A$' lies on $X$-axis and '$B$' lies on $Y$-axis. If $P$ is a point on $AB$ such that $PA=b$ and $PB=a$,then the equation of the locus of $P$ is

Let $A\ (2, -3)$ and $B\ (-2, 1)$ be the vertices of a triangle $ABC$. If the centroid of this triangle moves on the line $2x + 3y = 1$,then the locus of the vertex $C$ is which line?