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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2000

  • question_answer
    The focus of the parabola\[{{y}^{2}}=5x+4y+1\]is:

    A)  (1, 2)                    

    B)         \[(-1,2)\]            

    C)         \[(1,-2)\]            

    D)         \[\left( \frac{1}{4},2 \right)\]

    E)  \[\left( -\frac{1}{4},2 \right)\]

    Correct Answer: D

    Solution :

    \[{{y}^{2}}=5x+4y+1\] \[\Rightarrow \]               \[{{y}^{2}}-4y+4=5x+1+4\] \[\Rightarrow \]                               \[{{(y-2)}^{2}}=5(x+1)\] Let                          \[y-2=Y\] and                        \[x+1=X\] \[\Rightarrow \]                               \[{{Y}^{2}}=5X\] Here                      \[a=\frac{5}{4}\] \[\therefore \] Focus is                 \[(X=a,\text{ }Y=0)\] i.e.,        \[\left( x=\frac{5}{4}-1,y=2 \right)\] \[\Rightarrow \]               focus\[=\left( \frac{1}{4},2 \right)\]


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