Comprehension \( \quad \) Consider a hyperbola \( x y=4 \) and a line \( y+2 x=4, O \) is the ce...

Comprehension \( \quad \) Consider a hyperbola \( x y=4 \) and a line \( y+2 x=4, O \) is the centre of hyperbola. Tangent at any point \( P \) of hyperbola intersect the coordinate axes at \( A \) and \( B \).
Locus of circumcentre of triangle \( O A B \) is
(a) An ellipse with eccentricity \( \frac{1}{\sqrt{2}} \)
(b) An ellipse with eccentricity \( \frac{1}{\sqrt{3}} \)
(c) A hyperbola with eccentricity \( \sqrt{2} \)
(d) A circle