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Question
Find the locus of a point equidistant from the point (2, 4) and the y-axis.
Solution
Let P(h, k) be the point which is equidistant from the point (2, 4) and the y-axis.
The distance of point P(h, k) from the y-axis is h.
\[\therefore h = \sqrt{\left( h - 2 \right)^2 + \left( k - 4 \right)^2}\]
\[ \Rightarrow h^2 - 4h + 4 + k^2 - 8k + 16 = h^2 \]
\[ \Rightarrow k^2 - 4h - 8k + 20 = 0\]
Hence, the locus of (h, k) is
\[y^2 - 4x - 8y + 20 = 0\].
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