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

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it meets the conjugate hyperbola in imaginary points.

the conjugate diameter meets the given hyperbola in real point

he conjugate diameter meets the conjugate hyperbola in imaginary points.

none of these

answer is A.

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Detailed Solution

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

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