KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    The lines \[y=-\frac{3}{2}x\] and \[y=-\frac{2}{5}x\] intersect the curve \[3{{x}^{2}}+4xy+5{{y}^{2}}-4=0\] at the points P and Q respectively. The tangents drawn to the curve at P and Q:

    A) intersect each other at angle of \[45{}^\circ \]

    B) are parallel to each other

    C) are perpendicular to each other

    D) none of these

    Correct Answer: C

    Solution :

    \[\frac{dy}{dx}=\frac{2y+3x}{2x+5y}\] \[\Rightarrow \] \[{{\left. \frac{dy}{dx} \right]}_{{{x}_{1}}{{y}_{1}}}}=0\] & \[{{\left. \frac{dy}{dx} \right]}_{{{x}_{2}}{{y}_{2}}}}=\infty \]\[\Rightarrow \] tangents are perpendicular

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