The locus of the incentre of the triangle formed by the lines $xy-4x-4y+16=0$ and $x+y=5$ is

The locus of the centroid of the triangle whose vertices are $(a \cos t, a \sin t)$,$(b \sin t, -b \cos t)$,and $(1, 0)$,where $t$ is a parameter,is:

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

Let $a \neq 0, b \neq 0, c$ be three real numbers and $L(p, q) = \frac{ap + bq + c}{\sqrt{a^2 + b^2}}, \forall p, q \in \mathbb{R}$. If $L\left(\frac{2}{3}, \frac{1}{3}\right) + L\left(\frac{1}{3}, \frac{2}{3}\right) + L(2, 2) = 0$,then the line $ax + by + c = 0$ always passes through the fixed point:

$A$ straight line passing through a point $(3, 2)$ cuts the $X$ and $Y$-axes at points $A$ and $B$ respectively. If a point $P(h, k)$ divides $AB$ in the ratio $2: 3$,then the equation of the locus of point $P$ is

Show that the path of a moving point such that its distances from two lines $3x - 2y = 5$ and $3x + 2y = 5$ are equal is a straight line.