AP EAPCET 19-Aug-2021 Shift 2 Paper

In ΔABC AB:2x+3y−1=0
AC:x+2y+1=0
BC:ax+by−1=0
AD:(2x+3y−1)+λ(x+2y+1)=0
AD passes through origin
⇒−1+λ=0
or λ = 1
∴ AD,3x+5y=0
∵ AD⊥BC
⇒(

−3

5

)(

−a

b

)=−1 ‌‌‌‌‌ [m1.m1=−1]
⇒3a+5b=0 ...(i)
Again, BE,(2x+3y−1)+µ(ax+by−1)=0
BE passes through origin
⇒−1−µ=0
⇒µ=−1
BE,(2−a)x+(3−b)y=0
∵ BE ⊥ AC
⇒(

−1

2

)−(

2−a

3−b

)=−1
⇒a+2b=8 ...(ii)
Soving Eqs. (i) and (ii), we get
a=−40,b=24
∴

1

a

+

1

b

=

−1

40

+

1

24

=

1

60