question_answer

    The equation of the parabola with vertex at \[(-1,1)\]and focus (2, 1) is

A)  \[{{y}^{2}}-2y-12x-11=0\]

B)  \[{{x}^{2}}+2x-12y+13=0\]

C)  \[{{y}^{2}}-2y+12x+11=0\]

D)  \[{{y}^{2}}-2y-12x+13=0\]

Correct Answer: A

Solution :

                By the condition of parabola \[P{{M}^{2}}=P{{S}^{2}}\] \[\Rightarrow \]               \[{{(x+4)}^{4}}={{(x-2)}^{2}}+{{(y-1)}^{2}}\] \[\Rightarrow \]               \[{{x}^{2}}+8x+16={{x}^{2}}-4x+4+{{y}^{2}}-2y+1\] \[\Rightarrow \]               \[{{y}^{2}}-2y-12x-11=0\]