A particle moves along the curve x 2 = 2y . At what point, ordinate

increases at the same rate as abscissa increases?

A particle moves along the curve x^2 = 2y. At what point, ordinate

Question 23 - CBSE Class 12 Sample Paper for 2020 Boards - Part 2
Question 23 - CBSE Class 12 Sample Paper for 2020 Boards - Part 3

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Transcript

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. 𝑑𝑥/𝑑𝑡 "=" 𝑑𝑦/𝑑𝑡 and we need to find (x, y) Now, x2 = 2y Differentiating w.r.t. t 2x 𝑑𝑥/𝑑𝑡 = 2𝑑𝑦/𝑑𝑡 2x 𝑑𝑥/𝑑𝑡 = 2𝑑𝑥/𝑑𝑡 2x = 2 x = 1 Finding y Putting x = 1 in the equation x2 = 2y 12 = 2y (As 𝑑𝑥/𝑑𝑡 "=" 𝑑𝑦/𝑑𝑡) 1 = 2y 1/2 = y y = 1/2 So, required point is (1, 𝟏/𝟐)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.