question_answer

The equation of the parabola with focus (3, 0) and the directirx \[x+3=0\] is     [EAMCET 2002]

A)            \[{{y}^{2}}=3x\]                         

B)            \[{{y}^{2}}=2x\]

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

D)            \[{{y}^{2}}=6x\]

Correct Answer: C

Solution :

           \[\because \]\[S{{P}^{2}}=P{{M}^{2}}\] Þ\[{{(x-3)}^{2}}+{{y}^{2}}={{\left| \frac{x+3}{\sqrt{1}} \right|}^{2}}\]                    Þ\[{{x}^{2}}+9-6x+{{y}^{2}}={{x}^{2}}+9+6x\]                    Þ\[{{y}^{2}}=12x\].