Embibe Experts Solutions for Chapter: Pair of Straight Lines, Exercise 1: Exercise 1

If the lines joining the origin to the intersection of the line $y=mx+2$ and the circle $x^2+y^2=1$ are at right angles, then

The angle between the pair of lines whose equation is $4x^2+10xy+m{y}^2+5x+10y=0$ is

Equation of a line which is parallel to the line common to the pair of lines given by $6x^2-xy-12y^2=0$ and $15x^2+14xy-8y^2=0$ and at a distance $7$ units from it, is

If two pairs of lines $x^2-2mxy-y^2=0$ and $x^2-2nxy-y^2=0$ are such that one of them represents the bisector of the angles between the other, then

Distance between the pair of straight lines $x^2+6xy+9y^2+4x+12y-5=0$ is given by

The set of values of $m$ for which it is possible to draw the chord $y=\sqrt{m}x+1$ to the curve $x^2+2xy+\left(2+{\sin }^2\alpha \right)y^2=1,$ which subtends a right angle at the origin for some value of $\alpha$ is

Let the equation of the pair of lines, $y=px$ and $y=qx,$ can be written as $\left(y-px\right)\left(y-qx\right)=0.$ Then the equation of the pair of the angle bisectors of the lines $x^2-4xy-5y^2=0$ is:

If the lines represented by the equation $3y^2-x^2+\sqrt{3}x-3=0$ are rotated about the point $\left(\sqrt{3},0\right)$ through an angle of ${15}^{°},$ one clockwise direction and other in anti-clockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is