All chords of the curve 3x2-y2-2x+4y = 0 that subtends a right angle at the origin, pass through a fixed point whose coordinates are
The correct option is D (1, −2)
Let the equation of chord by y = mx + c. Combined equation of line joining the point intersection with origin is
These lines will be mutually perpendicular, if
3c + 2m – c + 4 = 0
⇒ 2m + 2c = −4
⇒ m + c = −2
That means the chord y = mx + c is always pass through the point (1, −2).
Hence, (a) is the correct answer.