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Question -

Find the locus of a point which moves such that its distance from the origin is three times is distance from x-axis.



Answer -

Let P (h, k) be any point on the locus and let A (0, 0) and B (h, 0).
Where, PA = 3PB

Now by squaring on both the sides we get,

h2 + k2 = 9k2

h2 = 8k2

By replacing (h, k) with (x, y)

Thelocus of point is x2 = 8y2

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