$A$ variable line $\frac{x}{a}+\frac{y}{b}=1$ is such that $a+b=4$. The locus of the midpoint of the portion of the line intercepted between the axes is

The locus of a point $P$ which moves such that the sum of its distances from two perpendicular lines is equal to $1$ is a

The locus of the point $P(x, y)$ such that the area of the $\triangle PAB$ is $7$,where $A(4, 5)$ and $B(-2, 3)$ are given points,is

$A$ line passing through the point $(1, 2)$ meets the axes at $P$ and $Q$ such that it forms a triangle $OPQ$,where $O$ is the origin. If the area of triangle $OPQ$ is minimum,then the slope of the line $PQ$ is:

$p, x_1, x_2, \ldots, x_n$ and $q, y_1, y_2, \ldots, y_n$ are two arithmetic progressions with common differences $a$ and $b$ respectively. If $\alpha$ and $\beta$ are the arithmetic means of $x_1, x_2, \ldots, x_n$ and $y_1, y_2, \ldots, y_n$ respectively,then the locus of $P(\alpha, \beta)$ is

$A$ point $P$ moves on the line $2x - 3y + 4 = 0$. If $Q(1, 4)$ and $R(3, -2)$ are fixed points,then the locus of the centroid of $\Delta PQR$ is a line