Find the locus of a point whose distance from the point $(1, 2)$ is equal to its distance from the aaxis of $y$ .

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Solution

Let the point $(x, y)$
Now,
Its distance from $y - a x i s = x$
Hence

$\sqrt{(x - 1)^{2} + (y - 2)^{2}} = x$
On squaring both the sides

$x^{2} + 1 - 2 x + y^{2} + 4 - 4 y = x^{2}$

$y^{2} - 4 y + 4 = 2 x - 1$

$(y - 2)^{2} = (4 \times \frac{1}{2}) \times (x - \frac{1}{2})$

It is a parabola

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