The locus of a point whose distance from the x-axis is one third of its distance from the origin is
A
x2=8y2
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B
y2=8x2
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C
x2=9y2
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D
y2=9x2
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Solution
The correct option is Ax2=8y2 Let an arbitrary point be P(x,y). Its distance from x-axis is dx=|y| and its distance from the origin is d=√x2+y2 It is given that dx=d3 or 3dx=d or 9d2x=d2 or 9(y2)=x2+y2 or x2−8y2=0