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JCECE Engineering JCECE Engineering Solved Paper-2011

  • question_answer
    If any tangent to the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] intercepts equal lengths I on the axes, then equals to

    A) \[{{a}^{2}}+{{b}^{2}}\]                  

    B) \[\sqrt{{{a}^{2}}+{{b}^{2}}}\]

    C) \[{{({{a}^{2}}+{{b}^{2}})}^{2}}\]                

    D)  None of these

    Correct Answer: B

    Solution :

    The equation of any tangent to the given ellipse is                 \[\frac{x}{a}\cos \theta +\frac{y}{b}\sin \theta =1\] This line meets the coordinate axes at                 \[P\left( \frac{a}{\cos \theta },\,\,0 \right)\]and\[Q\left( 0,\,\,\frac{b}{\sin \theta } \right)\]


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