Question

5. Write down the equation of the pair of straight lines joining the origin to the points of
intersection of the line 6x - y +8 =0 with the pair of straight lines
3x2 + 4xy - 4y - 11x + 2y + 6 = 0. Show that the lines so obtained make equal angles
with the coordinate axes.
​

Answer 1

Answer:

3x−y−2=0 or

2

3x−y

=1.

Making the equation of the curve homogenous, we get

7x

2

−4xy+8y

2

+(2(x−2y)

2

(3x−y)

−8⋅(

2

3x−y

)

2

=0

or (7x

2

−4xy+8y

2

)+(3x

−

7xy+2y

2

)−2(9x

2

−6xy+y

2

)=0

or −8x

2

+xy+8y

2

=0 is the required equation to the lines.

Since a+b=−8+8=0, and hence the lines are perpendicular.