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)
Therefore the equation of line in normal form:
ii)
Therefore the equation of line in normal form:
iii)
Therefore the equation of line in normal form:
vi)
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:
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:
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:
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:
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:
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:
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:
Therefore the equation of line in normal form:
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:
Therefore the equation of line in normal form:
Therefore equation of