the condition that the chord xcosA +ysinA-p=0 of x^2 +y^2-a=0 may subtend a right angle at the centre of the circle

Question

Vikas TU · Answer

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

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the condition that the chord xcosA +ysinA-p=0 of x^2 +y^2-a=0 may subtend a right angle at the centre of the circle

the condition that the chord xcosA +ysinA-p=0 of x^2 +y^2-a=0 may subtend a right angle at the centre of the circle

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the condition that the chord xcosA +ysinA-p=0 of x^2 +y^2-a=0 may subtend a right angle at the centre of the circle

the condition that the chord xcosA +ysinA-p=0 of x^2 +y^2-a=0 may subtend a right angle at the centre of the circle

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