Manipal Engineering Manipal Engineering Solved Paper-2015

  • question_answer
    The equations of the straight lines passing through the point (4, 3) and making intercepts on the coordinate axes whose sum is -1, is

    A)                                                                                    \[y=x,x=e,y=\frac{1}{x}\] and                                                                                               \[\frac{1}{2}\]

    B) \[\frac{3}{2}\]and \[\frac{5}{2}\]

    C) \[\underset{x\to \infty }{\mathop{\lim }}\,{{\left\{ \frac{a_{1}^{1/x}+a_{2}^{1/x}+...+a_{n}^{1/x}}{n} \right\}}^{nx}},\]and\[{{a}_{1}}+{{a}_{2}}+...+{{a}_{n}}\]

    D)  None of the above

    Correct Answer: A

    Solution :

    Let the equation of the line be                                                                                 \[\frac{x}{a}+\frac{y}{b}=1\] ...(i) which passes through (4, 3). \[\therefore \]\[\frac{4}{a}+\frac{3}{b}=1\]                                                        ...(ii) It is given that a + b = -1                  .. .(iii) On solving Eqs. (i) and (ii), we get \[a=-2,b=1\]or\[a=2,b=-3\] On substituting the values of a and b in Eq. (i), we get\[\frac{x}{-2}+\frac{y}{1}=1\]and\[\frac{x}{2}+\frac{y}{-3}=1\]


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