if the two of the lines given by 3x³+3x²y-3xy²+αy³=0 are at right angles,then the slope of one of them is

a.-1

b.1

c.3

d.-3

Hi Menka,

Note that the given cubic passes through the origin.

So the three lines will be of the form y=mx --------(Sub in the eqn, you'll get a cubic in m)

Now say m1,m2,m3 are the roots of the cubic.

And also use m1m2=-1

Write the sum, product, produce two at a time for the cubic eqn.

You'll get (m1)^2 = (m2)^2 = 1

and also m3=1.....

The solpe of one of the perpendicular lines could be (+1) or (-1)

The slope of the other line must be 1.

Best Regards,

Ashwin (IIT Madras).