AP EAMCET Engineering 2018 Apr 23 Shift 2 Paper

The equation of the line perpendicular to the line ax+by−1=0 and passes through origin is,
bx−ay=0 .....(I)
Now, altitude passes through the intersection of the line 2x+3y−1=0 and x+2y−1=0
So,
−b−a=0
a+b=0 ....(II)
From above the line ax+by−1=0 becomes,
x−y−

1

a

=0 ....(III)
Now, the altitude perpendicular to the line 2x+3y−1=0 and passes through origin is,
3x=2y
The point of intersection line (III) and x+2y−1=0 is,
(

1

3

(1+

2

a

),

1

3

(1−

1

a

)) satisfy the line,
a=−8‌and‌b=8
Thus, (a,b)=(−8,8)