Dr. SK Goyal Solutions for Chapter: Pair of Straight Lines, Exercise 5: INTRODUCTORY EXERCISE 3.5

If the straight lines joining origin to the points of intersection of the line $x+y=1$ with the curve $x^2+y^2+x-2y-m=0$ are perpendicular to each other, then the value of $m$ should be :

The pair of straight lines joining the origin to the common points of $x^2+y^2=4$ and $y=3x+c$ are perpendicular, if $c^2=$

Mixed term $xy$ is to be removed from the general equation of second degree $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$, one should rotate the axes through an angle $\theta$, then $\tan 2\theta$ is equal to :

The equation of the line joining the origin to the point of intersection of the lines $2x^2+xy-y^2+5x-y+2=0$ is :

Find the equation of the lines joining the origin to the points of intersection of $3x-2y=1$ with $3x^2+5xy-3y^2+2x+3y=0$ and show that they are at right angles.

If the straight line joining the origin and the points of intersection of $y=mx+1$ and $x^2+y^2=1$ be perpendicular to each other, find the value of $m$.

Prove that the straight lines joining the origin to the points of intersection of the straight line $kx+hy=2 hk$ with the curve ${\left(x-h\right)}^2+{\left(y-k\right)}^2=c^2$ are at right angles, if $h^2+k^2=c^2$.

Show that for all values of $\lambda$, the lines joining the origin to the points common to $x^2+2hxy-y^2+gx+fy=0$ and $fx-gy=\lambda$ are at right angles.