Скачать или смотреть Conic Section Hyperbola 23 ,

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1. A circle cuts the rectangular hyperbola 𝒙𝒚=𝟏 "in the points " (𝒙_𝒓,𝒚_𝒓 ), 𝒓=𝟏,𝟐,𝟑,𝟒. Prove that 𝒙_𝟏 𝒙_𝟐 𝒙_𝟑 𝒙_𝟒=𝒚_𝟏 𝒚_𝟐 𝒚_𝟑 𝒚_𝟒=𝟏.
2. If four points be taken on a rectangular hyperbola such that the chords joining any two points perpendicular to the chord joining the other two and if 𝜶,𝜷,𝜸 & 𝜹 be the inclinations to either asymptote of the lines joining these points and centre , prove that 𝒕𝒂𝒏𝜶 𝒕𝒂𝒏𝜷 𝒕𝒂𝒏𝜸 𝒕𝒂𝒏𝜹=𝟏.

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