Show that all the chords of the curve 3x2-y2-2x+4y=0 which subtend a right angle at the origin pass through a fixed point. Find that point.

Let y=mx + c be the equation of chord
Homogenize the equation of curve 3x²-y²-2x+4y=0 by putting 1= (y-mx)/c
Equation becomes 3x²-y²-2x(y-mx)/c+4y(y-mx)/c=0
Homogenization gives the equation of pair lines from origin on the given curve
Since the angle subtended at origin by the chord is 90⁰ . Angle between pair of line is 90⁰.
Condition for that is sum of coefficient of x² and y² in the homogenized equation is equal to 0.
Hence it will give after simpllication c + m +2=0
On rearranging -2= 1.m + C ….….….…....(1)
Compariing with y = mx + c
(1) passes through a fixed point (1,-2)