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KVPY Sample Paper KVPY Stream-SX Model Paper-4

  • 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 :

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


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