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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2009

  • question_answer
    The number of values of c such that the line \[y=4x+c\]touches the curve \[\frac{{{x}^{2}}}{4}+{{y}^{2}}=1\] is

    A)  \[1\]                                    

    B)  \[2\]

    C)  \[\infty \]                                          

    D)  \[0\]

    Correct Answer: B

    Solution :

    Given, \[y=4x+c\] and \[\frac{{{x}^{2}}}{4}+{{y}^{2}}=1\] Condition for tangency,                 \[{{c}^{2}}={{a}^{2}}{{m}^{2}}+{{b}^{2}}\] \[\therefore \]  \[{{c}^{2}}=4{{(4)}^{2}}+{{1}^{2}}\] \[\Rightarrow \]               \[{{c}^{2}}=65\] \[\Rightarrow \]               \[c=\pm \sqrt{65}\] Hence, for two values of c, the line touches the curve.


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