R D Sharma Solutions for Chapter: The Straight Lines, Exercise 18: EXERCISE 23.18

Find the equations of the straight lines passing through $\left(2,-1\right)$ and making an angle of $45°$ with the line $6x+5y-8=0$.

Find the equations to the straight lines which pass through the point $(h,k)$ and are inclined at angle ${\tan }^{-1}m$ to the straight line $y=mx+c$.

Find the equations to the straight lines passing through the point $(2,3)$ and inclined at an angle of $45°$ to the line $3x+y-5=0$.

Find the equations to the sides of an isosceles right angled triangle the equation of whose hypotenuse is $3x+4y=4$ and the opposite vertex is the point $(2,2)$

The equation of one side of an equilateral triangle is $x-y=0$ and one vertex is $(2+\sqrt{3},5)$. Prove that a second side is $y+(2-\sqrt{3})x=6$ and find the equation of the third side.

Find the equations of the two straight lines through $(1,2)$ forming two sides of a square of which $4x+7y=12$ is one diagonal.

Show that the point $(3,-5)$ lies between the parallel lines $2x+3y-7=0$ and $2x+3y+12=0$ 

The equation of the base of an equilateral triangle is $x+y=2$ and its vertex is $(2,-1)$. Find the length of its sides.