Sponsor Area

Application Of Derivatives

Question
CBSEENMA12035059

Find the slope of the tangent to the curve x = at2, y = 2at at  t = 1.

Solution

The curve is x = at2, y = 2at
therefore space space space space dx over dt space equals space 2 at comma space space dy over dt space equals space 2 straight a comma space space space space space space space space space space space space space space space therefore space space space space dy over dx space equals fraction numerator begin display style dy over dt end style over denominator begin display style dx over dt end style end fraction space equals fraction numerator 2 straight a over denominator 2 at end fraction space equals 1 over straight t
therefore space space space space value space of space dy over dx at space straight t space equals 1 space is space equals space 1 over 1 space equals space 1
Hence space the space slope space of space the space tangent space of space the space curve space at space straight t space equals space 1 space is space 1.