Question

The straight lines joining the origin to the points of intersection of 3x2 – 5xy – 3y2 + lambdax + 3y = 0 and 3x – 2y = 1 are at right angles, then value of lambda is​

Answer 1

Answer:

By application of the method of homogenization we get

3x

2

+mxy−4x(2x+y)+1(2x+y)

2

=3x

2

+mxy−8x

2

−4xy+4x

2

+y

2

+4xy

=−x

2

+mxy+y

2

=0

Hence the equations of the lines is given by x

2

−mxy−y

2

=0

Hence the lines are perpendicular for all values of m..