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If a diameter of a hyperbola meets the hyperbola in real points then
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Equation of the hyperbola be x2a2−y2b2=1 so equation of the conjugate hyperbola is x2a2−y2b2=−1Equation of a diameter of the hyperbola is y=b2/a2mx which meets the hyperbola at points given byx2a2−b4x2b2a4m2=1⇒x2=a2m2m2−b2These points are real if m2>b2 and for this value of m, the diameter will meet the conjugate hyperbola at point for which x2=−a2m2m2−b2 and these points are imaginary.Note: Conjugate diameter will meet the conjugate hyperbola in real points and the hyperbola in imaginary pointsTalk to our academic expert!
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