Question

finde the joint equation of pair of lines through the origin and making an angle of 6 with the line 3x+y-6=0 in deep method​

Answer 1

Answer:

There are three terms having degree 2.

Hence, trying to solve those at first.

x2−3xy+2y2

=x2−2xy−xy+2y2

=x(x−2y)−y(x−2y)

=(x−y)(x−2y)

Now other linear and constant terms will be due to a and b.

(x−y+a)(x−2y+b)=x2−3xy+2y2+x−2

or,bx+ax+ab−by−2ay=x−2

or,(a+b)x+ab−(2a+b)y=x−2

a+b=1… (i)

2a+b=0 .. (ii)

Subtracting (i) from (ii)

a=−1

Then, b=2

So,

(x−y−1)(x−2y+2)=0

Either,

x−y−1=0

or,

x−2y+2=0

If both are zero simultaneously we can find solution,

y−3=0

y=3 andx=4

Step-by-step explanation: