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BCECE Engineering BCECE Engineering Solved Paper-2004

  • question_answer
    The curve represented by\[x=3(\cos t+\sin t),y=4(\cos t-\sin t)\]is:

    A)  ellipse                 

    B)         parabola            

    C)         hyperbola      

    D)         circle

    Correct Answer: A

    Solution :

    We have \[\frac{x}{3}=(\cos t+\sin t),\frac{y}{4}=(\cos t-\sin t)\] On squaring and adding, we get \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{16}=2({{\cos }^{2}}t+{{\sin }^{2}}t)\] \[\Rightarrow \]               \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{16}=2\] \[\Rightarrow \]               \[\frac{{{x}^{2}}}{18}+\frac{{{y}^{2}}}{32}=1\] Which represents the equation of an ellipse.


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