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