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BCECE Engineering BCECE Engineering Solved Paper-2005

  • question_answer
    The equation of line parallel to the tangent to the circle \[{{x}^{2}}+{{y}^{2}}={{r}^{2}}\]at the point \[({{x}_{1}},{{y}_{1}})\] and passing through origin, is:

    A) \[x{{y}_{1}}+{{x}_{1}}y=0\]

    B)         \[x{{x}_{1}}-y{{y}_{1}}=0\]

    C)                         \[x{{x}_{1}}+y{{y}_{1}}=0\]

    D)         \[xy-{{x}_{1}}y=0\]

    Correct Answer: C

    Solution :

    As we know that tangent on point \[({{x}_{1}},{{y}_{1}})\]of the circle \[{{x}^{2}}+{{y}^{2}}={{r}^{2}}\]is \[xx{{ & }_{1}}+y{{y}_{1}}={{r}^{2}}\]               ?(i) The required line is parallel to the tangent line i.e.,          \[x{{x}_{1}}+y{{y}_{1}}=k\] Since, it is passing through origin \[\Rightarrow \]    \[k=0\] \[\therefore \]\[x{{x}_{1}}+y{{y}_{1}}=0\]


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