AP EAPCET 25-Aug-2021 Shift 2 Paper

Given, equation of lines
x2+2hxy+2y2=0 ...(i)
On comparing with ax2+2hxy+by2=0
⇒ a=1 and b=2
Le1 y=m1x and y=m2x be the lines, whose
combined form is Eq. (i)
∴ m1+m2=

−2h

b

=

−2h

2

=−h ...(ii)
and m1m2=

a

b

=

1

2

...(iii)
∵ m1:m2=1:2
⇒

m1

m2

=

1

2

⇒m2=2m1
From Eq. (ii), we get m1+m2=−h and from
Eq. (iii) we get
m1+2m1=−h and m1m2=

1

2

m1=−

h

3

and 2m12=

1

2

⇒ −

h

3

=±

1

2

⇒ h=±

3

2

and m1=

±1

2