Dr. SK Goyal Solutions for Chapter: The Straight Lines, Exercise 11: FILL IN THE BLANKS

If the point $P\left(a^2,a\right)$ lies in the region corresponding to the acute angle between the line $2y=x$ and $4y=x$, then $a\in \left(m,4\right)$, where $m$ is  _____

The point $\left(1+\cos \theta ,\sin \theta \right)$ lies between the region corresponding to the acute angle between the lines $x-3y=0$ and $x-6y=0$. If $\theta \in \left(2n\pi +2{\tan }^{-1}\left(\frac{1}{m}\right),2n\pi +2{\tan }^{-1}\left(\frac{1}{n}\right)\right)$, then $m+n$ is equal to  _____

One of the bisector of the angle between the lines $a{\left(x-1\right)}^2+2h\left(x-1\right)\left(y-2\right)+b{\left(y-2\right)}^2=0$ is $x+2y-5=0$. Then other bisector is _____.

If the lines $2\left(\sin a+\sin b\right)x-2\sin \left(a-b\right)y=3$
$2\left(\cos a+\cos b\right)x+2\cos \left(a-b\right)y=5$ are perpendicular, then $\sin 2a+\sin 2b$ is equal to _____

If the sum of the distances of a point from two perpendicular lines in a plane is $1,$ then its locus is:

The incentre of triangle formed by the lines $x=0, y=0$ and $3x+4y=12$ is -

A family of lines is given by the equation $\left(3x+4y+6\right)+\lambda \left(x+y+2\right)=0$. The line situated at the greatest distance from the point $\left(2,3\right)$ belonging to this family has the equation _____ .

If $3a+2b+6c=0$, the family of straight lines $ax+by+c=0$ passes through a fixed point whose coordinates are given by