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LetP (h,K) be anypointon curve y=f(x). Lettangentdrawnat point P meets x-axis at T & normal atpoint P meets x-axis at N(as shown in figure) and m =(dy)/(dx)]_()(h,k)) = shope of tangent. (i)Length of tangent =PT =|K| sqrt(1+(1)/(m^(2))) (ii) Length of Normal =PN +|K| sqrt(1+m^(2)) (iii) Length subtangent = Projection of segment PT on x-axis =TM =|(k)/(m)| (iv) Length of subnormal=Projection of line segment PN on x-axis =MN =|Km| Findlengthof subnormalto x=sqrt(2) cos t,y =- 3sin t " at " t= (-pi)/(4). |
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Answer» `(2)/(9)` |
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