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A curve is given by the equations `x=sec^2theta,y=cotthetadot`If the tangent at `Pw h e r etheta=pi/4`meets the curve again at `Q ,t h e n[P Q]`is, where [.] represents the greatest integer function, _________. |
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Answer» Correct Answer - 3 `(dy)/(dx)=(-1)/2cot^(3)theta-(-1)/2` at `theta=(pi)/4` Also, the point `p` for `theta=(pi)/4` is `(2,1)` equation of tangen is`y-1=(-1)/2(x-2)` This meets the curve whose ccartesian equation on eliminating `theta` by `sec^(2)theta-tan^(2)theta=1` is `y^(2)=1/(x-1)` solving (1) and (2), we get `y=1, (-1)/2` `:.x=2,5` Hence `P` is `(2,1)` given and `Q` is `(5,(-1)/2)` Therefore `PQ=-sqrt(45/4)=(3sqrt(5))/2 [PQ]=3` |
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