Question

Find K if the equation represents a pair of lines x^(2)-y^(2)+2x+k=0​

Answer 1

Answer:

Given equation is 3x

2

+10xy+3y

2

+16y+k=0

Comparing it with ax

2

+2hxy+by

2

+2gx+2fy+c=0

We get, a=3,h=5,b=3,g=0,f=8,c=k

The equation represents pair of straight lines.

∴ abc+2fgh−af

2

−bg

2

−ch

2

=0

⇒ 3×3×k+2×8×0×5−3(8)

2

−3(0)

2

−k(5)

2

=0

⇒ 9k+0−192−0−25k=0

⇒ −16k−192=0

⇒ −16k=192

∴ k=−12