CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2003

  • question_answer
    If the slope of one of the lines given by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] is 5 times the other then:

    A)  \[5{{h}^{2}}=9ab\]                         

    B)  \[5{{h}^{2}}=ab\]

    C)  \[{{h}^{2}}=ab\]                             

    D)  \[9{{h}^{2}}=5ab\]

    Correct Answer: A

    Solution :

    Let (he slope of first line be m then slope of second line is 5m. Then \[m+5m=-\frac{2h}{b}\]and \[m\,.\,5m=\frac{a}{b}\] \[\Rightarrow \]               \[m=-\frac{2h}{6b}\]                 \[=-\frac{h}{3b}\] \[\therefore \]  \[5{{m}^{2}}=\frac{a}{b}\] \[\Rightarrow \]               \[5{{\left( -\frac{h}{3b} \right)}^{2}}=\frac{a}{b}\] \[\Rightarrow \]               \[\frac{5{{h}^{2}}}{9{{b}^{2}}}=\frac{a}{b}\] \[\Rightarrow \]               \[5{{h}^{2}}=9ab\]


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