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JEE Main & Advanced Sample Paper JEE Main Sample Paper-22

  • question_answer
    C is a curve defined by the parametric equation \[x\text{ }=\text{ }{{t}^{2}}\] and \[y={{t}^{3}}-3t.\]The equation of the tangent line to this curve at (4, 2) is

    A)  \[y=15x-58\]                

    B)  \[y=2\]

    C)  \[y=x-2\]         

    D)   \[y=\frac{9x}{4}-7\]

    Correct Answer: D

    Solution :

    Slope \[M=\frac{dy}{dx}=\frac{dy/dt}{dx/dt}\] \[\therefore \,\,M=\frac{3{{t}^{2}}-3}{2t}\,=t=2\] \[\Rightarrow \,\,M=\frac{9}{4}\] Equation of tangent at (4, 2) is \[M=\frac{9}{4}\] \[\therefore \,\,(y-2)=\frac{9}{4}(x-4)\Rightarrow \,\,y=\frac{9}{4}x-7\]


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