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

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

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

If two of the three lines represented by ax^3+ bx^2y +cxy^2+dy^3=0 may be at right angles then

If two of the three lines represented by ax^3+ bx^2y +cxy^2+dy^3=0 may be at right angles then

If two of the three lines represented by ax^(3)+bx^(2)y+cxy^(2)+dy^(3)=0 may be at right angles then

The length of the sides of a triangle are ax-by , ay+bx and sqrt((a^2+b^2)(x^2+y^2)) . Show that it is a right angled triangle.

Find the condition that two of the three lines represented by ax^3+bx^2y+cxy^2+dy^3=0 may be at right angle.

y_(1) and y_(2) and y_(3) are the ordinates of three points on the parabola y ^(2) = 4ax, then the area of the triangle formed by the points is-