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

There are two candles of same length and same size. Both of them burn at uniform rate. The first one burns in $5\,hr$ and the second one burns in $3\,h$. Both the candles are lit together. After how many minutes the length of the first candle is $3$ times that of the other?

Draw a quadrilateral in the Cartesian plane, whose vertices are $(-4,5),(0,7) (5,-5)$ and $(-4,-2) .$ Also, find its area.

If the three lines $x - 3y = p, ax + 2y = q$ and $ax + y = r$ form a right-angled triangle then

If the straight line $ax + by + c = 0$ always passes through $(1, -2),$ then $a, b, c$ are

A straight line through the point $(1, 1)$ meets the $x$-axis at ‘$A$’ and the $y$-axis at ‘$B$’. The locus of the mid-point of $AB$ is