Locus (1 Viewer)

[vice lord]

A circle passing though the origin O is tangent to the hyperbola xy = 1 at A , and intersects the hyperbola again at 2 distinct points B and C . Prove OA is perpendicular to BC

 

[Aerath]

I don't even understand how this question is possible....A circle with centre at origin, and a tangent to the hyperbola xy=1, would be tangent to both halves of the hyperbola, no?

 

[gurmies]

I don't even understand how this question is possible....A circle with centre at origin, and a tangent to the hyperbola xy=1, would be tangent to both halves of the hyperbola, no?

It's not centered at the origin, it just passes through it. (x-a)^2 + (y-b)^2 = r^2, with the condition a^2 + b^2 = r^2.

 

[Aerath]

Oh. Yeah. Misread the question.