question_answer

The equation of the tangent at the point \[(a\sec \theta ,\ b\tan \theta )\] of the conic \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], is

A)            \[x{{\sec }^{2}}\theta -y{{\tan }^{2}}\theta =1\]                        

B)            \[\frac{x}{a}\sec \theta -\frac{y}{b}\tan \theta =1\]

C)            \[\frac{x+a\sec \theta }{{{a}^{2}}}-\frac{y+b\tan \theta }{{{b}^{2}}}=1\]

D)            None of these