AP EAPCET 24-Aug-2021 Shift 2 Paper

Given, equation of pair of straight line
2x2+axy+3y2=0
and 2x2+bxy−3y2=0
Let the slope of line m and m1 of the equation
2x2+axy+3y2=0
∴ m+m1=

−a

3

and mm1=

2

3

Slope of the other line is m and m2.
Then, m+m2=

b

3

and mm2=−

2

3

Given, m1m2=−1 ...(i)
∴

mm1

mm2

=−1
⇒m1=−m2
⇒m1+m2=0 ...(ii)
From Eqs.(i) and (ii), we get
m1=1 and m,=−1
∴m=

2

3

m+m1=−

a

3

⇒

2

3

+1=−

a

3

⇒a=−5
and m+m2=

b

3

⇒

2

3

−1=

b

3

⇒b=−1
∴ a=−5 and b=−1