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The equation of the normal at the point $(a\sec \theta ,\;b\tan \theta )$ of the curve ${b^2}{x^2} - {a^2}{y^2} = {a^2}{b^2}$ is

• A
  $\frac{{ax}}{{\cos \theta }} + \frac{{by}}{{\sin \theta }} = {a^2} + {b^2}$
• B
  $\frac{{ax}}{{\tan \theta }} + \frac{{by}}{{\sec \theta }} = {a^2} + {b^2}$
• ✓
  $\frac{{ax}}{{\sec \theta }} + \frac{{by}}{{\tan \theta }} = {a^2} + {b^2}$
• D
  $\frac{{ax}}{{\sec \theta }} + \frac{{by}}{{\tan \theta }} = {a^2} - {b^2}$