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if the two of the lines given by 3x 3 +3x 2 y-3xy 2 +αy 3 =0 are at right angles,then the slope of one of them is a.-1 b.1 c.3 d.-3

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

Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

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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