question_answer

If (0, 6) and (0, 3) are respectively the vertex and focus of a parabola, then its equation is               [Karnataka CET 2004]

A)            \[{{x}^{2}}+12y=72\]                 

B)            \[{{x}^{2}}-12y=72\]

C)            \[{{y}^{2}}-12x=72\]                 

D)            \[{{y}^{2}}+12x=72\]

Correct Answer: A

Solution :

           Here vertex \[\equiv \](0, 6) and focus \[\equiv \] (0, 3)            then \[Z\equiv (0,\,9)\] i.e.,  \[y=9\]            \[\therefore \] Equation of parabola, \[SP=PM\]            \[\Rightarrow \] \[\sqrt{{{(x-0)}^{2}}+{{(y-3)}^{2}}}=|y-9|\]            \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}-6y+9={{y}^{2}}-18y+81\]            or \[{{x}^{2}}+12y=72\].