Question 1
Question: Find the value of 'a' for which the lines ax + 4y + 5 = 0 and 9x + ay - 4 = 0 are parallel to each other.
Answer: ax + 4y + 5 = 0 and 9x + ay - 4 = 0 are parallel to each other, the slopes are equal.
Question 2
Question: Find the equation of the line perpendicular to the line 8x + 5y = 7 and passing through (1, 2).
Answer: 
(
Product of slopes of two perpendicular lines = -1)
Aliter:
Given line is 8x + 5y = 7.
The line perpendicular to 8x + 5y = 7 is 5x - 8y = k.
This line passes through (1,2).
The required equation of the line is
5x - 8y = -11 or 5x - 8y + 11 = 0
Question 3
Question: Find the equation of the line, which bisects the line joining (3, -1) and (5,11) and also bisects the distance between the points (-5,2) and (9,6).
Answer: The co-ordinates of the middle point of the line joining (3,-1) and (5,11) is
Let P (4,5) be the point.
The co-ordinates of the middle point of the line joining (-5,2) and (9, 6) is
Let Q (2,4) be the point.
We have to find the equation of the line joining the points P and Q.
Question 4
Question: 
Answer: 
\ The required equation is
Question 5
Question: Find the image of the point (-1,1) w.r.t to the line 3x + 4y = 32.
Answer: 
Let the image of the point P (-1,1) about the line AB be Q (h,k).
PQ is perpendicular to AB and is bisected at C.
Solving (ii) and (i) for h and k, we have
Reflection of P (-1,1) about the line 3x + 4y = 32 is
Question 6
Question: Find the co-ordinates of the foot of the perpendicular from the point (4, -1) on the line x + 4y = 2.
Answer: 
Slope of line perpendicular to x + 4y = 2 is 4.
The point of intersection of the line given the co-ordinates of the foot of perpendicular is
Question 7
Question: Find the equation of two lines passing through the point (4,5) 
Answer: The equation of the line through (4,5) with slope m is
y - 5 = m(x - 4)
The slope of line 2x - y + 7 = 0 is 2.
The required lines are
Question 8
Question: Find the equation of the line, which makes intercepts of 2 and 3 with x-axis and y-axis respectively.
Answer: Here,
a = 2, b = 3
The required equation of the line is
Question 9
Question: Find the equation of the straight line which passes through (4,5) and sum of intercepts on the coordinate axes is 18.
Answer: Let the intercept on the x-axis be a, then the intercept on the y-axis will be (18 - a).
The line passes through (4,5).
a = 8 or a = 9
When a = 8, b = 9 or when a = 9, b = 8
The required equations are
Question 10
Question: Find the equation of the line through (a,b) and the sum of the intercepts on the coordinate axes is 2(a+b).
Answer: Let s be the intercept on the x-axis, then the intercept on y-axis will be
2(a + b) - s.
Let t = 2(a+b)-s
This passes through (a,b).
Equation of the line is
