Arun
Last Activity: 6 Years ago
The diameter thro ( 1/2, 2/5 ) has equation y=(4/5)x
The conjugate diameter has gradient m given by m*(4/5) = −16/25 → m=−4/5
All chords parallel to this are bisected by y=(4/5)x so chord of interest has m=−4/5
∴ its equation is y−2/5 = (−4/5)(x−1/2) → y = (4/5)(1−x)
This intersects ellipse when x²/25 + (16/25)(1−x)²/16 = 1
This simplifies to x²−x−12 = 0 which has solutions x=4 or −3
Using chord equation, the ends of chord are thus (4,−12/5) & (−3,16/5)
Length of chord is thus √( 7² + (28/5)² ) = (7/5)√41
