There are two sets of parallel lines, their equations being `x cos alpha + y sin alpha = p`; p =1,2,3,....,m and `y cos alpha - x sin alpha = q`; q = 1,2,3,....,n(n> m) where a given constant. Show that the lines form `1/6 m (m-1) (3n-m-1)` squares

There are two sets of parallel lines, their equations being x cos alpha+y sin alpha=p and x sin alpha- y cos alpha=p , p=1,2,3,….n and alpha in (0,pi//2) . If the number of rectangles formed by these two sets of lines is 225 , then the value of n is equals to

There are two sets of parallel lines, their equations being x cos alpha+y sin alpha=p and x sin alpha- y cos alpha=p , p=1,2,3,….n and alpha in (0,pi//2) . If the number of rectangles formed by these two sets of lines is 225 , then the value of n is equals to (a) 4 (b) 5 (c) 6 (d) 7

There are two sets of parallel lines, their equations being x cos alpha+y sin alpha=p and x sin alpha- y cos alpha=p , p=1,2,3,….n and alpha in (0,pi//2) . If the number of rectangles formed by these two sets of lines is 225 , then the value of n is equals to (a) 4 (b) 5 (c) 6 (d) 7

The distance between two parallel lines is p^(1)-p equation of one line is x cos alpha+y sin alpha=p then the equation of the 2^(nd) line is

The lines x cos alpha + y sin alpha = p_1 and x cos beta + y sin beta = p_2 will be perpendicular, if :

The lines x cos alpha + y sin alpha = P_1 and x cos beta + y sin beta = P_2 will be perpendicular, if :

The lines x cos alpha + y sin alpha = P_1 and x cos beta + y sin beta = P_2 will be perpendicular, if :

The lines x cos alpha + y sin alpha = P_1 and x cos beta + y sin beta = P_2 will be perpendicular, if :

The lines x cos alpha + y sin alpha = P_1 and x cos beta + y sin beta = P_2 will be perpendicular, if :