All chords of the curve  3x2−y2−2x+4y=0, which subtend a right angle at the origin, pass through the fixed point. The square of its distance from the origin is

Given curve is 3x2−y2−2x+4y=0…………..(1)Let the equation of the chord lx+my=1………. (2)Homogenising (1) with the help of (2) we get 3x2−y2−(2x−4y)(lx+my)=0coefficient of x2 + coefficient of y2 = 0 ⇒ℓ−2m=1…………(3)from (2) and (3), we get (x,y) = (1, -2)square of distance from (1,-2) to (0,0) 12+(−2)2=5