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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).
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