A) \[{{y}^{2}}=ax\]
B) \[{{y}^{2}}=2ax\]
C) \[{{y}^{2}}=4ax\]
D) \[{{x}^{2}}=4ay\]
Correct Answer: B
Solution :
Any line through origin (0,0) is \[y=mx\]. It intersects \[{{y}^{2}}=4ax\] in \[\left( \frac{4a}{{{m}^{2}}},\frac{4a}{m} \right)\]. Mid point of the chord is \[\left( \frac{2a}{{{m}^{2}}},\frac{2a}{m} \right)\] \[x=\frac{2a}{{{m}^{2}}},\]\[y=\frac{2a}{m}\]Þ \[\frac{2a}{x}=\frac{4{{a}^{2}}}{{{y}^{2}}}\] or \[{{y}^{2}}=2ax\], which is a parabola.
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