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Rectangular Hyperbola

In hyperbola 75424.png If a = b, then it is called rectangular hyperbola, whose equation is given as x2 – y2 = a2.
When the above hyperbola is rotated by an angle 45° about origin in anticlockwise direction, then its equation becomes xy = c2, where c2 = 2a2.
Properties of rectangular hyperbola
  • Eccentricity of rectangular hyperbola is 75418.png.
  • Parametric form of rectangular hyperbola xy = c2 is P(ctc/t), where t  R – {0}.
  • Equation of tangent at point whose parameter is “t” is x + yt2 – 2ct = 0.
  • Equation of normal at “t” is xt3 – yt – ct4 + c = 0.
  • Equation of tangent at (x1y1) is xy1 + xx1 = 2c2.
  • Equation of normal at (x1y1) is xx1 – yy1 = x12 – y12.

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