A) \[{{(x+a)}^{2}}=\frac{1}{2}(2y-2b)\]
B) \[{{(x-a)}^{2}}=\frac{1}{2}(2y-2b)\]
C) \[{{(x+a)}^{2}}=\frac{1}{4}(2y-2b)\]
D) \[{{(x-a)}^{2}}=\frac{1}{8}(2y-2b)\]
Correct Answer: A
Solution :
[a] The parabola having the axis parallel to the y-axis is \[{{(x-a)}^{2}}=4A(y-b)\] According to the question, the length of latus rectum is 4A=1. Hence, the equation of the parabola is \[{{(x-a)}^{2}}=1(y-b)\] Or \[{{(x-a)}^{2}}=\frac{1}{2}(2y-2b)\]
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