+91-87964 74404
FlagBACK
Question icon
Grade 12th PassAnalytical Geometry

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

Profile image of Menka Malguri
14 Years agoGrade 12th Pass
Answers icon

1 Answer

Profile image of Ashwin Muralidharan IIT Madras
14 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).

Other Related Questions on analytical geometry

question mark
  • The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is 
analytical geometry
1 Answer Available

Last Activity: 4 Years ago

question mark
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
analytical geometry
1 Answer Available

Last Activity: 4 Years ago

question mark
show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0
analytical geometry
1 Answer Available

Last Activity: 4 Years ago

question mark
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius. 
 
analytical geometry
1 Answer Available

Last Activity: 4 Years ago

question mark
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
analytical geometry
1 Answer Available

Last Activity: 4 Years ago