Question

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

Answer 1

The given curve is

3x² - y² - 2x + 4y = 0    ....(i)

Let y = mx + c be the chord of curve (i) which subtend right angle at origin. Then, the combined equation of lines joining points of intersection of curve (i) and chord y = mx + c to the origin, can be obtained by the equation of the curve homogeneous. ie,

Since, the lines represented are perpendicular to each other.