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Question
Find the locus of a point which moves such that its distance from the origin is three times its distance from the x-axis.
Solution
Let P(h, k) be a point. Let O(0, 0) be the origin.
So, the distance of point P(h, k) from the x-axis is k.
\[ \Rightarrow h^2 + k^2 = 9 k^2 \]
\[ \Rightarrow h^2 = 8 k^2\]
Hence, the locus of (h, k) is \[x^2 = 8 y^2\].
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