Mathematics
Describe the locus of a point P, so that :
AB2 = AP2 + BP2,
where A and B are two fixed points.
Locus
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Answer
We know that,
Angle subtended by a diameter on any point of a circle is 90°.
From figure,
By pythagoras theorem,
⇒ Hypotenuse2 = Perpendicular2 + Base2
⇒ AB2 = AP2 + BP2
We know that,
Pythagoras theorem applies on right angle triangle.
∴ AP ⊥ BP.
Hence, the locus of the point P is the circumference of a circle with AB as diameter.
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