All chords of the curve which subtend a right angle at the origin, pass through the fixed point
Explanation for the correct answer:
Step 1: Finding the equation from the chord.
The curve is --------- (1)
Let the equation, be the chord of the given curve that subtends the right angle at the origin.
Step 2: Substitute the chord equation in 1.
The equation of the intersection of the curve and the chord is
becomes
The coefficients of and
Step 3: Finding the coordinate:
The curve and the chord are perpendicular to each other.
So the slope,
Here, then
On comparing the equations and with the equation of chord, we get
Thus the point is the fixed point through which the curve passes through the origin subtends a right angle.
Hence, option (B) is the correct answer.