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A particle moves along the curve x ^{ 2 } = 2y . At what point, ordinate
increases at the same rate as abscissa increases?
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CBSE Class 12 Sample Paper for 2020 Boards
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CBSE Class 12 Sample Paper for 2020 Boards
Last updated at March 16, 2023 by Teachoo
Get live Maths 1-on-1 Classs - Class 6 to 12
Question 23 A particle moves along the curve x2 = 2y . At what point, ordinate increases at the same rate as abscissa increases? Given curve x2 = 2y We need to point (x, y) where ordinate increases at the same rate as abscissa increases i.e. ππ₯/ππ‘ "=" ππ¦/ππ‘ and we need to find (x, y) Now, x2 = 2y Differentiating w.r.t. t 2x ππ₯/ππ‘ = 2ππ¦/ππ‘ 2x ππ₯/ππ‘ = 2ππ₯/ππ‘ 2x = 2 x = 1 Finding y Putting x = 1 in the equation x2 = 2y 12 = 2y (As ππ₯/ππ‘ "=" ππ¦/ππ‘) 1 = 2y 1/2 = y y = 1/2 So, required point is (1, π/π)