Embibe Experts Solutions for Chapter: Point and Straight Line, Exercise 1: Exercise 1

Locus of the middle point of the intercept on the line  $y=x+c$  made by the lines $2 x+3 y=5$ and $2 x+3 y=8, c$ being a parameter, is -

A ray of light is sent along the line $x-2 y-3=0$ on reaching the line $3 x-2 y-5=0$ the ray is reflected from it, then the equation of the line containing the reflected ray is

In an isosceles triangle $ABC$, the coordinate of the points $B$ and $C$ on the base $BC$ are respectively $(1,2)$ and $(2,1)$. If equation of line $AB$ is $2 x-y=0$, then slope of line $AC$ is

The number of lines which pass through the point $(2,-3)$ and are at distance $7$ units from point $(-1,2)$ is

The line $2 x+3 y=12$ meet the $x$-axis at $A$ and $y$-axis at $B$. The line through $(5,5)$ perpendicular to $AB$ meets the $x$-axis, $y$-axis and the given line at $C, D$ and $E$ respectively. If $O$ is the origin of coordinates, then three times the area of $OCEB$ is

Locus of the points which are at equal distances from $3 x+4 y-11=0$ and $12 x+5 y+2=0$ and which is near to the origin is $ax+by-133=0$ then $a+b$ is equal to

The distance between the pair of parallel lines $x^2+2xy+y^2-8ax-8ay-9a^2=0$ is $\left(ka\right)$ units then $k^2$ is equal to -

If $(a+3b)(3a+b)=4h^2$, then the angle between the lines represented by $a{x}^2+2hxy+b{y}^2=0$ is $\theta$ then the value of ${\sec }^2\theta +5{\cot }^2\frac{\theta }{2}$ is equal to