EAMCET Engineering 2001 Solved Paper

The given lines are and
x+3y‌=10 . . . (i)
and 6x2+xy−y2‌=0

or ‌‌6x2+3xy−2xy−y2=0
or ‌‌3x(2x+y)−y(2x+y)=0
3x−y=0 . . . (ii)
2x+y=0 . . . (iii)
On solving Eqs. (i) and (ii), we get
⇒‌x+3⋅(3x)‌=10
⇒‌10x‌=10
‌‌ and ‌‌x‌=1
⇒‌3⋅1−y‌=0
‌‌ Coordinates of ‌B‌ are ‌(1,3)‌
On solving Eqs. (ii) and (iii), we get
x=0,y=0
∴ Coordinates of A are (0,0).
A line perpendicular to BC is
3x−y=λ
It passes through (0,0), then 0−0=λ
⇒‌‌λ=0
The line AD is ‌‌3x−y=0 . . . (iv)
A line perpendicular to AC is
x−2y=λ
It passes through (1,3), then 1−6=λ
λ=−5
The line BE is ‌‌x−2y=−5 . . . (v)
On solving Eqs. (iv) and (v), we get
x=1,y=3
Thus, the coordinates of required orthocentre is (1,3).