Prove that the straight lines y + x = c and y = x + d are at right angles, whatever be the angle between the axes.

If the three lines x-3y=p,ax+2y=q and ax+y=r from a right-angled triangle then:

The angle between the lines y=x and y=-x+6 is

What is the angle between the lines x+y=1 and x-y=1 ?

Prove that the curves y^(2)=4ax and xy=c^(2) cut at right angles if c^(4)=32a^(4) .

If the portion of the line ax - by - 1 = 0 , intercepted between the lines ax + y + 1 = 0 and x + by = 0 subtends a right angle at the origin , then find value of 4a +b^2 + (b+1)^2 .

The portion of the line x+3y-1 =0 intersepted between the lines ax+y+1 = 0 and x + 3y =0 subtend a right angle at origin , then the value of |a| is