Note: The equation of the line whose length of the perpendicular from the origin is and the angle made by the perpendicular with the positive x-axis is given by is given by

Question 1: Find the Equation of a line for which

i)      ii)      iii)      vi)

Answer:

i)       Given

Therefore the equation of line in Normal form:

  

ii)      Given

Therefore the equation of line in normal form:

iii)    Given

Therefore the equation of line in normal form:

vi)     Given

Therefore the equation of line in normal form:

Question 2: Find the equation of the line on which the length of the Perpendicular segment from the origin to the line is and the inclination of the perpendicular segment with the positive direction of x-axis is .

Answer:

Given

Therefore the equation of line in normal form:

Question 3: Find the equation of the line whose perpendicular distance from the origin is units and the angle which the normal makes with the positive direction of x-axis is .

Answer:

Given

Therefore the equation of line in normal form:

Question 4: Find the equation of the straight line at a distance of units from the origin such  that the perpendicular from the origin to the line makes an angle given by with the positive direction of x-axis.

Answer:

Given

           

  and 

Therefore the equation of line in normal form:

Question 5: Find the equation of the straight line on which the length of the perpendicular from the origin is and the perpendicular makes an angle with x-axis such that .

Answer:

Given

Therefore the equation of line in normal form:

Question 6: Find the equation of the straight line upon which the length of the perpendicular from the
origin is and the slope of this perpendicular is .

Answer:

Given

  and 

Therefore the equations of line in normal form:

Case 1:

Case 2:

Question 7: The length of the perpendicular from the origin to a line is and the line makes an angle of with the positive direction of y-axis. Find the equation of the line.

Answer:

Given

Therefore the equation of line in normal form:

Question 8: Find the value of   and  , if the equation   is the normal form  of the line .

Answer:

Given equation is

Comparing this with the equation we get

     

Question 9: Find the equation of the straight line which makes a triangle of area with the axes and perpendicular from the origin to it makes an angle of with y-axis.

Answer:

Given

Therefore the equation of line in normal form:

Therefore x-intercept    and   y-intercept

It is given that the area of

Therefore equation of

Question 10: Find the equation of a straight line on which the perpendicular from the origin makes an angle of with x-axis and which forms a triangle of area with the axes

Answer:

Given

Therefore the equation of line in normal form:

Therefore x-intercept   and   y-intercept

It is given that the area of

Therefore equation of