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All chords of the curve 3x^2-y^2-2x+4y=0...

All chords of the curve `3x^2-y^2-2x+4y=0` which subtend a right angle at the origin, pass through the fixed point

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Statement-1: All chords of the curve 3x^(2)-y^(2)-2x+4y=0 which subtend a right angle at the origin pass through a fixed point. Statement-2: The equation ax+by+c=0 represents a family of straight lines passing through a fixed point iff there is a linear relation between a, b and c.

Show that all chords of the curve 3x^(2)-y^(2)-2x+4y=0, which subtend a right angle ax the origin,pass through a fixed point.Find the coordinates of the point.

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Show that all the chords of the curve 3x^2 – y^2 – 2x + 4y = 0 which subtend a right angle at the origin are concurrent. Does this result also hold for the curve, 3x^2 + 3y^2 – 2x + 4y = 0 ? If yes, what is the point of concurrency and if not, give reasons.

All the chords of the curve 2x^(2) + 3y^(2) - 5x =0 which subtend a right angle at the origin are concurrent at :

The locus of the foot of the perpendicular, from the origin to chords of the circle x^(2)+y^(2)-4x-6y-3=0 which subtend a right angle at the origin,is: