Equation of auxiliary circle of hyperbola same as its conjugate
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Its transverse and conjugate axes are along y and x axes respectively. The equation of the conjugate hyperbola to xy = c2 is xy = –c2. The equation of the hyperbola and asymptotes differ by the same constant by which the equations of the asymptotes and the conjugate hyperbola differ.
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A cricle drawn with centre C and transverse axis as a diameter is called the auxiliary circle of the hyperbola. The equation of the auxiliary circle is x2 + y2 = a2.
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