Question 1
Question: If p is the length of perpendicular drawn from the origin on the line AB whose intercepts on the axes are a and b, then show 
Answer: 
Aliter:
Equation of the line AB in the intercept form is
...(i)
Since (i) and (ii) represent the same line, we have
Squaring and adding, we get
Question 2
Question: A straight line passes through the point (a, b) and this bisects the part of the line intercepted between the axes.
Show that 
Answer: 
Let the straight line passing through p(a, b) cut the x-axis at A(a,0) and B(0,b) on the x-axis and the y-axis respectively.
Question 3
Question: Find the equation of the straight line which passes through the point (2,3) and whose intercepts on the y-axis is thrice that on the x-axis.
Answer: Let the equation of the line in the intercept form be
From the problem, b = 3a.
(ii) passes through (2,3).
b = 3a = 3 x 3 = 9
Question 4
Question: Find the equation of the straight line which passes through the point (3,2) and cuts off intercepts a and b respectively on the x and y axis such that a - b = 2.
Answer: Let the equation of the line be
...(i)
From the problem, a - b = 2
a = b+2
This line passes through (3,2).
The two lines are
Question 5
Question: Find the equation of the line which makes thrice the intercepts made by the line 3x + 4y = 12 on the coordinate axes.
Answer: The given line is 3x+4y = 12. ......(i)
The intercept made by the line on the x-axis is obtained by substituting
y = 0 in (i).
The intercept made by the line on the y-axis is obtained by substituting
x = 0 in (i).
The intercepts made by the required line are 3a and 3b.
i.e. 12 and 9 respectively.
Equation of the required line is
Note:
Question 6
Question: Find the equation of the straight line, which passes through p(1,-7) and meets the axes at A and B respectively, so that 4AP - 3BP = 0, where O is the origin.
Answer: 
Now, the point p(1,-7) divides AB in the ratio AP:PB::3:4.
Let the coordinates of A be (a,0) and that of B be (0,b).
The equation of the line is
Question 7
Question: 
Answer: Let C divide AB in the ratio m:n. The coordinates of C are
Since lies on ax + by + c = 0, we have
which is the required ratio.
Question 8
Question: Find the equations of the diagonals of the quadrilateral whose 
ratio in which each diagonal divides the other.
Answer: 
Equation of diagonal AC is
or
Let this line divide DB in the ratio m:n.
Equation of the diagonal BD is
Let this line divide the diagonal AC in the ratio m:n.
Question 9
Question: Find the equation of the line passing through (2,-1) and making an angle of 45o with the positive direction of the x-aixs. Also find the points on the line at a distance
from the point (2,-1).
Answer: Here,
Equation of the line is
y + 1 = 1(x - 2)
x - y = 3
Question 10
Question: Find the equation of the line which passes through the point
points on the line that is 5 units away from the point (3,2).
Answer:
The equation of the line in the point-slope form is
Here,
The points on the line at a distance 5 units from (3,2).
The points are (7,5) and (-1,-1).
