↵The condition that the chord xcos(alpha) + ysin(alpha) - p = 0 may subtend a right angle at the centre of the circle x2 + y2 - a2 = 0 is
- a2 = 2p2
- p2 = 2a2
- a = 2p
- p = 2a
Hi,
xcosα + ysinα = p
The perp ON from O to line has length |0+0−p|/√(cos²α+sin²α) = |p|
If chord of intersection AB subtends 90° at centre then ∠NOB=45°
From ΔNOB, cos(45°) = |p|/a → a=|p|√2 or a²=2p²
xcosα + ysinα = p
The perp ON from O to line has length |0+0−p|/√(cos²α+sin²α) = |p|
If chord of intersection AB subtends 90° at centre then ∠NOB=45°
From ΔNOB, cos(45°) = |p|/a → a=|p|√2 or a²=2p²