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KVPY Sample Paper KVPY Stream-SX Model Paper-5

  • question_answer
    The shortest distance from the line \[3x+4y=25\] to the circle \[{{x}^{2}}+{{y}^{2}}=6x-8y\] is equal to

    A) 7/5       

    B) 9/5

    C) 11/5                             

    D) 32/5

    Correct Answer: A

    Solution :

    [a]
    Equation of circle \[{{x}^{2}}+{{y}^{2}}-6x+8y=0\]
    \[{{(x-3)}^{2}}+{{(y+4)}^{2}}=25\]
    Centre \[(3,-\,4),\]radius = 5
    Distance from \[(3,-\,4)\]to the line \[3x+4y-25=0\]is \[d=\left| \frac{9-16-25}{5} \right|=\frac{32}{5}\]
    Shortest distance \[=d-r=\frac{32}{5}-5=\frac{7}{5}\]
                           


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