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Question
Find the locus of a point which is equidistant from (1, 3) and the x-axis.
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Solution
Let P(h, k) be a point that is equidistant from A(1, 3) and the x-axis.
Now, the distance of the point P(h, k) from the x-axis is k.
\[\therefore\] AP = K
\[\Rightarrow A P^2 = k^2\]
\[\Rightarrow \left( h - 1 \right)^2 + \left( k - 3 \right)^2 = k^2 \]
\[ \Rightarrow h^2 - 2h + 1 + k^2 - 6k + 9 = k^2 \]
\[ \Rightarrow h^2 - 2h - 6k + 10 = 0\]
Hence, the locus of (h, k) is
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