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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The axis of the parabola \[9{{y}^{2}}-16x-12y-57=0\] is [MNR 1995]

    A)            \[3y=2\]                                    

    B)            \[x+3y=3\]

    C)            \[2x=3\]                                    

    D)            \[y=3\]

    Correct Answer: A

    Solution :

               Since \[9{{y}^{2}}-16x-12y-57=0\]                    Þ \[{{\left( y-\frac{2}{3} \right)}^{2}}=\frac{16}{9}\left( x+\frac{61}{16} \right)\]                    Put \[y-\frac{2}{3}=Y\]and \[x+\frac{61}{16}=X\]Þ \[{{Y}^{2}}=4\left( \frac{4}{9} \right)\,X\]                    Axis of this parabola is \[Y=0\]Þ \[y-\frac{2}{3}=0\]Þ\[3y=2\].


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