2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Applications of Derivatives

JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Tangent and Normal

  • question_answer
    The angle of intersection of curves \[y={{x}^{2}},\] \[6y=7-{{x}^{3}}\] at (1, 1) is [Kurukshetra CEE 2002]

    A)            \[\pi /4\]

    B)            \[\pi /3\]

    C)            \[\pi /2\]

    D)            \[\pi \]

    Correct Answer: C

    Solution :

               \[y={{x}^{2}}\] Þ \[{{\left( \frac{dy}{dx} \right)}_{(1,\,1)}}={{m}_{1}}=2x=2\]            \[6y=7-{{x}^{3}}\Rightarrow 6\,.\,\frac{dy}{dx}=-3{{x}^{2}}\] Þ\[{{\left( \frac{dy}{dx} \right)}_{(1,\,1)}}={{m}_{2}}=-\frac{1}{2}\]            Clearly \[{{m}_{1}}{{m}_{2}}=-1,\] therefore angle of intersection is \[\frac{\pi }{2}\].


You need to login to perform this action.
You will be redirected in 3 sec spinner