Question 107
The two lines with slopes $2$ and $1/2$ pass through an arbitrary point $T$ on the axis $Oy$ and intersect the hyperbola $y = 1/x$ at four points.
a) Prove that these four points lie on a circle.
b) The point $T$ runs through the entire $y$-axis. Find the locus of the centers of such circles.
a) Prove that these four points lie on a circle.
b) The point $T$ runs through the entire $y$-axis. Find the locus of the centers of such circles.