G Tewani Solutions for Chapter: Straight Lines, Exercise 3: DPP

The equation of the line which is equally inclined to the axes and passes through common points of a family of lines $4acx+y(ab+bc+ca-abc)+abc=0$ where $a, b, c>0$ are in $\mathrm{H}.\mathrm{P}.$ is

The base $BC$ of a triangle $ABC$ is bisected at the point $(p, q)$ and the equations of the sides $AB$ and $AC$ are $px+qy=1$ and $qx+py=1$, respectively. The equation of the median through $A$ is

$A\left(x_1, y_1\right), B\left(x_2, y_2\right)$ and $C\left(x_3 ,y_3\right)$ are three vertices of a triangle $ABC.$ $lx+my+n=0$ is the equation of a line$L.$ If the centroid of the triangle $ABC$ is at the origin and algebraic sum of the lengths of the perpendiculars from the vertices of the triangle $ABC$ to the line $L$ is equal to $1,$ then the sum of the squares of reciprocals of the intercepts made by $L$ on the coordinate axes is equal to

A straight line passes through the point of intersection of  $x-2y-2=0$ and $2x-by-6=0$ and the origin, then the complete set of values of $b$ for which the acute angle between this line and $y=0$ is less than ${45}^{°}$, is

The locus of the foot of the perpendicular from the origin on each member of the family $(4a+3)x-(a+1)y-(2a+1)=0$ is 

Equation of the diagonals of a rectangle are $y+8x-17=0$ and $y-8x+7=0.$ If the area of the rectangle is $8$ sq. units, then the equation of the sides of the rectangle is/are

If $6a^2-3b^2-c^2+7ab-ac+4bc=0$, then the family of lines $ax+by+c=0, \left|a\right|+\left|b\right|\ne 0$ is concurrent at

If graph of $xy=1$ is reflected in $y=2x$ to give the graph $12x^2+rxy+s{y}^2+t=0,$ then