The Cartesian form of the polar equation $\theta = \tan^{-1} 2$ is

Every point $(x, y)$ on the curve $3x + 2y - 3xy = 0$ is the centroid of a triangle formed by the coordinate axes and a line $(L)$ intersecting both the coordinate axes. Then all such lines $(L)$

Let $P$ be a moving point such that the sum of its perpendicular distances from the lines $2x + y - 3 = 0$ and $x - 2y + 1 = 0$ is always $2 \, units$. Then,the area bounded by the locus of point $P$ is:

Let $P(2, 3)$,$Q(6, 0)$,and $R(\alpha, \beta)$ be three points in the $x-y$ plane such that $|PR + QR| + |PR - QR|$ is minimum. Then the value of $(\alpha - 2\beta)$ is:

If the line $\frac{x}{a} + \frac{y}{b} = 1$ is a variable line such that $\frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{c^2}$,then the locus of the foot of the perpendicular from the origin to the line is:

If a point $P$ on the line $3x + 5y = 15$ is equidistant from the coordinate axes,then $P$ lies