AP EAMCET Engineering 2018 Apr 24 Shift 1 Paper

The given equation of parabola is
14x2+38xy+20y2+x−7y−91=0
Factorize 14x2+38xy+20y2=0
(7x+5y)(2x+4y)=0
The first asymptote is 7x+5y−3=0
The second asymptote is 2x+4y+k=0
The combine equation of the asymptote is
(7x+5y−3)(2x+4y+k)=0
Compare the coefficient of x.
7k−6=1
k=1
Therefore, the equation of the above asymptote is 2x+4y+1=0