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UPSC CDS Math Circle Questions
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Question : 8
Total: 46
If a point P moves such that the sum of the squares of its distances from two fixed points A and B is a constant, then the locus of the point P is
[2018 CDS-II]
A straight line
A circle
Perpendicular bisector of AB
An arbitrary curve
Validate
Solution:
If point P lies on the circumference of a circle with diameter AB, then ∠APB = 90° (angle formed by diameter on a circle).
∴ AP^2+BP^2=AB^2(Pythagoras theorem)
Thus, the locus of point P is a circle.
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