Locus of the middle points of the chords of the hyperbola x 2 a 2 - y 2 b 2 =   1 which passes through a fixed point α ,   β is hyperbola whose centre is -

Step-by-step solution

T = S 1 at mid point h , k h x a 2 - k y b 2 = h 2 a 2 - k 2 b 2 pass α , β point ∴ h α a 2 – k y b 2 = h 2 a 2 – k 2 b 2 ∴ locus is x 2 - α x a 2 - y 2 - β y b 2 = 0 ⇒ x - α / 2 2 a 2 - y - β / 2 2 b 2 = 1 4 α 2 a 2 - β 2 b 2 = k 2 l e t is a hyperbola. Where centre is α / 2 , β / 2 .