# Rectangular Hyperbola

In hyperbola  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 .
• 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.