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JEE Main & Advanced JEE Main Paper (Held on 10-4-2019 Afternoon)

  • question_answer
    The tangent and normal to the ellipse \[3{{x}^{2}}+5{{y}^{2}}=32\]at the point P(2, 2) meet the x-axis at Q and R, respectively. Then the area (in sq. units) of the triangle PQR is : [JEE Main 10-4-2019 Afternoon]

    A) \[\frac{14}{3}\]                                  

    B) \[\frac{16}{3}\]

    C) \[\frac{68}{15}\]        

    D) \[\frac{34}{15}\]

    Correct Answer: C

    Solution :

    \[3{{x}^{2}}+5{{y}^{2}}=32\] \[{{\left. \frac{dy}{dx} \right|}_{(2,2)}}=-\frac{3}{5}\] Tangent : \[y-2=-\frac{3}{5}(x-2)\Rightarrow Q\left( \frac{16}{3},0 \right)\] Normal : \[y-2=\frac{5}{3}(x-2)\Rightarrow R\left( \frac{4}{5},0 \right)\] Area is \[=\frac{1}{2}(OR)\times 2=QR=\frac{68}{15}.\]            


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