A) \[{{x}^{2}}+12y=72\]
B) \[{{x}^{2}}-12y=72\]
C) \[{{y}^{2}}-12x=72\]
D) \[{{y}^{2}}+12x=72\]
Correct Answer: A
Solution :
Since, the focus and vertex of the parabola are on y-axis, therefore its directrix is parallel to x-axis and axes of the parabola is y-axis Let the equation of the directrix by \[y=k\] the directrix meets the axis of the parabola at (0, k). But vertex is the mid point of the line segment joining the focus to the point where directrix meets axis of the parabola \[\frac{k+3}{2}=6\,\,\,\,\,\Rightarrow k=9\] Thus the equation of directrix is \[y=9\] \[\therefore \] Equation of parabola is \[{{(x-0)}^{2}}+{{(y-3)}^{2}}={{(y-9)}^{2}}\] \[{{x}^{2}}+{{y}^{2}}-6y+9={{y}^{2}}-18y+81\] \[{{x}^{2}}+12y-72=0\]
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