Show that if two of the lines `ax^3 + bx^2y + cxy^2 + dy^3 = 0" "(a ne 0)` make complementary angles with X-axis in anticlockwise sense then a(a-c)+d(b-d) = 0.

Statement-I : If two of the lines represented by ax^(3) + bx^(2)y + cxy^(2) + dy^(3) = 0 (a ne 0) make complementary angles with x-axis in anti-clockwise sense then slope of third line is a/d. Statement-II : If the slope of one of the line represented by ax^(2) + 2hxy + by^(2) = 0 is 'n' times the slope of another then ((1+n)^(2))/(n)=(h^(2))/(a b) Which of the above statement is correct :

If the equation ax^3+3bx^2y+3cxy^2+dy^3=0 (a,b,c,d ne 0) represents three coincident lines then

Show that the sum of roots of a quadratic equation ax^(2) + bx + c = 0 (a ne 0) is (-b)/(a) .

The locus of the point of intersection of two tangents to the parabola y^(2)=4ax which make complementary angles with the axis of the parabola is

IF ax^2 + 2cx + b=0 and ax^2 + 2bx +c=0 ( b ne 0) have a common root , then b+c=

Show that pair of bisectors of angles between the lines (ax + by)^(2) = c(bx - ay)^(2) (c gt 0) are parallel and perpendicular to the line ax+by+k=0

Show that the condition that two of the three lines represented by ax^(3)+bx^(2)y+cxy^(2)+dy^(3)=0 may be at right angles is a^(2)+ac+bd+d^(2)=0

For a ne b ne c if the lines x + 2ay + a = 0 , x + 3by + b = 0 and x + 4cy + c = 0 ar concurrent , then a , b, c are in

Show that the sum of roots of a quadratic equation ax^(2)+bx+c=0 (a ne 0) is (-b)/(a) .