Dr. SK Goyal Solutions for Chapter: The Straight Lines, Exercise 6: INTRODUCTORY EXERCISE 2.6

The three sides of a triangle are given by $\left(x^2-y^2\right)\left(2x+3y-6\right)=0$. If the point $\left(-2, a\right)$ lies inside and $\left(b, 1\right)$ lies outside the triangle, then :

$A$ ray of light passing through the point $\left(1, 2\right)$ is reflected on the $x$ -axis at a point $P$ and passes through the point $\left(5, 3\right)$ then the abscissa of a point $P$ is

A ray of light travelling along the line $x+y=1$ is incident on the $x$-axis and after refraction it enters the other side of the $x$-axis by turning $\frac{\pi }{6}$ away from the $x$-axis. The equation of the line along which the refracted ray travels is :

All points lying inside the triangle formed by the points $(1,3),(5,0)$ and $(-1,2)$ satisfy

A light ray coming along the line $3x+4y=5,$ gets reflected from the line $ax+by=1$ and goes along the line $5x-12y=10,$ then

Two sides of a triangle have the joint equation $x^2-2xy-3y^2+8y-4=0$. The third side, which is variable, always passes through the point $\left(-5,-1\right)$. Find the range of values of the slope of the third side, so that the origin is an interior point of the triangle.

Let $P(\sin \theta ,\cos \theta )$, where $0\le \theta \le 2\pi$ to be a point and let$OAB$ be a triangle with vertices $(0,0), \left(\sqrt{\frac{3}{2}},0\right)$ and $\left(0,\sqrt{\frac{3}{2}}\right)$. Find $\theta$ if  $P$ lies inside the $∆OAB$. 

  Find all the values of $\theta$ for which the point $\left({\sin }^2\theta ,\sin \theta \right)$ lies inside the square formed by the lines $xy=0$ and $4xy-2x-2y+1=0$.