Question

AB is a fixed line. State the locus of the point P so that AB${}^2$= AP${}^2$+ BP${}^2$

• A. Circle with radius AB
• B. Circle with diameter AB
• C. Circle with diameter 3AB
• D. None of these

Answer 1

The correct option is B

Circle with diameter AB

P is such that AB ${}^2$= AP${}^2$+ BP${}^2$. So, $\Delta$ APB is a right angled triangle.

For a circle having diameter AB, the $\Delta$ APB is right angled for any point P lying on the circle.

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