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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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. ๐‘‘๐‘ฅ/๐‘‘๐‘ก "=" ๐‘‘๐‘ฆ/๐‘‘๐‘ก and we need to find (x, y) Now, x2 = 2y Differentiating w.r.t. t 2x ๐‘‘๐‘ฅ/๐‘‘๐‘ก = 2๐‘‘๐‘ฆ/๐‘‘๐‘ก 2x ๐‘‘๐‘ฅ/๐‘‘๐‘ก = 2๐‘‘๐‘ฅ/๐‘‘๐‘ก 2x = 2 x = 1 Finding y Putting x = 1 in the equation x2 = 2y 12 = 2y (As ๐‘‘๐‘ฅ/๐‘‘๐‘ก "=" ๐‘‘๐‘ฆ/๐‘‘๐‘ก) 1 = 2y 1/2 = y y = 1/2 So, required point is (1, ๐Ÿ/๐Ÿ)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.