1.

Find the locus of the point P such that the distance of P from the point A(4, 0) is twice the distance of P from the x-axis.

Answer»

Let P = (x, y). Distance of P from the x-axis is |y|. Therefore

AP = 2|y| ⇔ (AP)2 = 4y2

⇔ (x - 4)2 + y2 = 4y2

⇔ x2 - 3y2 - 8x + 16 = 0

Hence the equation of the locus is x2 - 3y2 - 8x + 16 = 0



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