A triangle is formed by $X -$ axis, $Y$ - axis and the line $3 x+4 y=60$. Then the number of points $P ( a, b)$ which lie strictly inside the triangle, where $a$ is an integer and $b$ is a multiple of $a$, is $...........$
$31$
$30$
$28$
$56$
The locus of the mid-points of the perpendiculars drawn from points on the line, $\mathrm{x}=2 \mathrm{y}$ to the line $\mathrm{x}=\mathrm{y}$ is
The orthocentre of the triangle formed by the lines $xy = 0$ and $x + y = 1$ is
The co-ordinates of the orthocentre of the triangle bounded by the lines, $4x - 7y + 10 = 0; x + y=5$ and $7x + 4y = 15$ is :
Show that the area of the triangle formed by the lines
$y=m_{1} x+c_{1}, y=m_{2} x+c_{2}$ and $x=0$ is $\frac{\left(c_{1}-c_{2}\right)^{2}}{2\left|m_{1}-m_{2}\right|}$.