1. Find the values of k for which the line (k–3) x – (4 – k2) y + k2 –7k + 6 = 0 is (a) Parallel to the xaxis,
(b) Parallel to the yaxis,
(c) Passing through the origin.
 
2. Find the values of θ and p, if the equation x cos θ + y sinθ = p is the normal form ...  
3. Find the equations of the lines, which cutoff intercepts on the axes whose sum and product are 1 and – 6, respectively.  
4. What are the points on the yaxis whose distance from the line
is ... 4 units.  
5. Find perpendicular distance from the origin of the line joining the points (cosθ, sin θ)
and (cos φ, sin φ).  
6. Find the equation of the line parallel to yaxis and drawn through the point ofintersection of the lines x – 7y + 5 = 0 and 3x + y = 0.  
7. Find the equation of a line drawn perpendicular to the line ... through the point, where it meets the yaxis.  
8. Find the area of the triangle formed by the lines y – x = 0, x + y = 0 and x – k = 0.
 
9. Find the value of p so that the three lines 3x + y – 2 = 0, px + 2 y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.
 
10. If three lines whose equations are y = m1x + c1, y = m2x + c2 and y = m
are concurrent, then show that ...  

11. Find the equation of the lines through the point (3, 2) which make an angle of 45 with the line x – 2y = 3.
 
12. Find the equation of the line passing through the point of intersection of the lines
4x + 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes  
13. Show that the equation of the line passing through the origin and making an angle θ with the line ...  
14. In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4?
 
15. Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x – y = 0.
 
16. Find the direction in which a straight line must be drawn through the point (–1, 2)
so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point.  
17. The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (– 4, 1). Find the equation of the legs (perpendicular sides) of the triangle.  
18. Find the image of the point (3, 8) with respect to the line x +3y = 7 assuming the
line to be a plane mirror.  
23. Prove that the product of the lengths of the perpendiculars drawn from the ...  
24. A person standing at the junction (crossing) of two straight paths represented by
the equations 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 wants to reach the path whose
equation is 6x – 7y + 8 = 0 in the least time. Find equation of the path that he
should follow.  
