question_answer

The equation of the parabola whose vertex is at (2, ?1) and focus at (2, ?3) is [Kerala (Engg.) 2002]

A)            \[{{x}^{2}}+4x-8y-12=0\]          

B)            \[{{x}^{2}}-4x+8y+12=0\]

C)            \[{{x}^{2}}+8y=12\]                   

D)            \[{{x}^{2}}-4x+12=0\]

Correct Answer: B

Solution :

           \[VS=\sqrt{{{(2-2)}^{2}}+{{(-3+1)}^{2}}}=2\]. From \[{{(x-h)}^{2}}=-4a(y-k)\] Parabola is,  \[{{(x-2)}^{2}}=-4.2(y+1)\] Þ \[{{(x-2)}^{2}}=-\,8(y+1)\] Þ \[{{x}^{2}}+4-4x=-8y-8\] Þ \[{{x}^{2}}-4x+8y+12=0.\]