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  • The orthocentre of the triangle formed by the points  <img alt="\mathrm{(\tan \theta, \cot \theta),(\operatorname{cosec} \theta, \sin \theta) \text { and }(\cos \theta, \sec \th

The orthocentre of the triangle formed by the points 

\mathrm{(\tan \theta, \cot \theta),(\operatorname{cosec} \theta, \sin \theta) \text { and }(\cos \theta, \sec \theta)}  is

Option: 1

(0,0)


Option: 2

(1,1)


Option: 3

(-1,-1)


Option: 4

\mathrm{\left(-\sec ^2 \theta,-\cos ^2 \theta\right)}


Answers (1)

best_answer

Clearly, the given three points lie on the curve xy=1

Here \mathrm{t_1=\tan \theta, t_2=\operatorname{cosec} \theta \text { and } t_3=\cos \theta}

\mathrm{\begin{aligned} \therefore \text { Orthocentre }=\left(\frac{-c}{t_1 t_2 t_3},-c t_1 t_2 t_3\right) & =\left(\frac{-1}{t_1 t_2 t_3},-t_1 t_2 t_3\right) \\ & =(-1,-1) \end{aligned}}

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Gaurav

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