Note: We know that the equations of two lines passing through   and making and angle   with the given line   are

Question 1: Find the equation of the straight lines passing through the origin and making an angle of with the straight line .

Answer:

We know that the equations of two lines passing through   and making and angle   with the given line   are

Here

Therefore the equation are:

     … … … … … i)

     … … … … … ii)

Therefore are the two equations.

Question 2: Find the equations to the straight lines which pass through the origin and are inclined at an angle of to the straight line .

Answer:

Given equation:

          

Here

Therefore the equations are:

     … … … … … i)

     … … … … … ii)

Therefore are the two equations.

Question 3: Find the equations of the straight lines passing through and making an angle of with the line .

Answer:

Given equation:

          

Here

Therefore the equations are:

     … … … … … i)

     … … … … … ii)

Therefore are the two equations.

Question 4: Find the equations to the straight lines which pass through the point and are inclined at angle to the straight line .

Answer:

Here

Therefore the equations are:

… … … … … i)

     … … … … … ii)

Therefore are the two equations.

Question 5: Find the equations to the straight lines passing through the point and inclined at an angle of to the line .

Answer:

Given equation:

          

Here

Therefore the equations are:

     … … … … … i)

     … … … … … ii)

Therefore are the two equations.

Question 6: Find the equations to the sides of an isosceles right angled triangle the equation of whose hypotenuse is and the opposite vertex is the point .

Answer:

Given equation:

          

Here

Therefore the equations are:

     … … … … … i)

     … … … … … ii)

Therefore are the two equations.

Question 7: The equation of one side of an equilateral triangle is and one vertex is . Prove that a second side is and find the equation of the third side.

Answer:

Refer to the adjoining figure. Since the triangle is equilateral triangle, hence all angles are

Given equation:

          

Here

Therefore the equations are:

     … … … … … i)

     … … … … … ii)

Therefore are the two equations.

Question 8: Find the equations of the two straight lines through forming two sides of a square of which is one diagonal.

Answer:

Refer to the adjoining figure.

Given equation:

          

Here

Therefore the equations are:

     … … … … … i)