what do you mean by conjugate diameter in hyperbola ...explain with diagram.................

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$$\begin{gathered} \mathrm{Two} \mathrm{diameters} \mathrm{of} \mathrm{a} \mathrm{conic} \mathrm{section} \mathrm{are} \mathrm{said} \mathrm{to} \mathrm{be} \mathrm{conjugate} \mathrm{if} \mathrm{each} \mathrm{chord} \mathrm{parallel} \mathrm{to} \mathrm{one} \\ \mathrm{diameter} \mathrm{is} \mathrm{bisected} \mathrm{by} \mathrm{the} \mathrm{other} \mathrm{diameter}. \\ \mathrm{For} \mathrm{example}, \mathrm{two} \mathrm{diameters} \mathrm{of} \mathrm{a} \mathrm{circle} \mathrm{are} \mathrm{conjugate} \mathrm{if} \mathrm{and} \mathrm{only} \mathrm{if} \mathrm{they} \mathrm{are} \mathrm{perpendicular}. \\ \mathrm{Hence} \mathrm{diameters} \mathrm{of} \mathrm{a} \mathrm{hyperbola} \mathrm{are} \mathrm{conjugate} \mathrm{when} \mathrm{each} \mathrm{bisects} \mathrm{all} \mathrm{chords} \mathrm{parallel} \mathrm{to} \mathrm{the} \mathrm{other}. \\ \mathrm{In} \mathrm{this} \mathrm{case} \mathrm{both} \mathrm{the} \mathrm{hyperbola} \mathrm{and} \mathrm{its} \mathrm{conjugate} \mathrm{are} \mathrm{sources} \mathrm{for} \mathrm{the} \mathrm{chords} \mathrm{and} \mathrm{diameters}. \\ \mathrm{In} \mathrm{the} \mathrm{figure} \mathrm{below} \mathrm{For} \mathrm{any} \mathrm{\phi }, \mathrm{the} \mathrm{indicated} \mathrm{hyperbolas} \mathrm{are} \mathrm{conjugate}. \end{gathered}$$


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