Question 21
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 22
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 23
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 24
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 25
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
