If a diameter of a hyperbola meets the hyperbola in real points then

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 points