Manipal Entrance Test 2016 Math Paper

Let ax+by=1 be the chord ...(i)
Making the equation of hyperbola homogeneous using Eq. (i), we get
3x2−y2+ (−2x+4y)(ax+by)=0
or (3−2a)x2+ (−1+4b)y2 +(−2b+4a)xy=0
Since, the angle subtended at the origin is a right angle
∴ Coefficient of x2+ Coefficient of y2=0
⇒(3−2a)+(−1+4b)=0
⇒a=2b+1
∴ Chords are (2b+1)x+by−1=0
or b(2+y)+(x−1)=0
which clearly pass through the fixed point (1,-2)