Statement I If a circle intersect a hyperbola at four points

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Statement I If a circle

S \equiv 0

intersect a hyperbola

xy = 4

at four points, three of them being

(2, 2)

(4, 1)

and

(6, 2/3)

, then the coordinates of the fourth point are

\left(\frac{1}{4}, 16\right)

. Statement II If a circle

S \equiv 0

intersects a hyperbola

xy = c^2

t_1, t_2, t_3

and

t_4

, then

t_1 t_2 t_3 t_4 = 1