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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?

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


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

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.