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Example - 3 : A and B are two fixed points in a plane. Find the locus of a point P which moves in such a way that PA² + PB² = AB².

Solution : PA² + PB² = AB² is true only when

Also, angle in a semi-circle is a right angle.

So, we draw a circle with AB as a diameter and take any point P on the cirlcle.

Hence, the locus of P is the circumference of a circle with AB as a diameter.