If t is a parameter,A = (a sec t, b tan t),B | vedclass

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(A) Let the centroid of $	riangle OAB$ be $(x, y)$.Since $O = (0, 0)$,$A = (a \sec t, b 	an t)$,and $B = (-a 	an t, b \sec t)$,the coordinates of t

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$9xy = ab$

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(A) Let the centroid of $	riangle OAB$ be $(x, y)$.Since $O = (0, 0)$,$A = (a \sec t, b 	an t)$,and $B = (-a 	an t, b \sec t)$,the coordinates of the centroid are given by:$x = \frac{0 + a \sec t - a 	an t}{3} \Rightarrow 3x = a(\sec t - 	an t) \dots (i)$$y = \frac{0 + b 	an t + b \sec t}{3} \Rightarrow 3y = b(	an t + \sec t) \dots (ii)$Multiplying equations $(i)$ and $(ii)$:$(3x)(3y) = a(\sec t - 	an t) \cdot b(\sec t + 	an t)$$9xy = ab(\sec^2 t - 	an^2 t)$Since $\sec^2 t - 	an^2 t = 1$,we get:$9xy = ab$.

If $t$ is a parameter,$A = (a \sec t, b \tan t)$,$B = (-a \tan t, b \sec t)$,and $O = (0, 0)$,then the locus of the centroid of $\triangle OAB$ is:

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