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Locus of the point P such that the sum of distances from two fixed points is always constant is __________

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Locus of the point P such that the sum of distances from two fixed points is always constant is __________

(a) an ellipse

(b) a hyperbola

(c) a parabola having those fixed point on its axis

(d) a line perpendicular to line joining those two points and passing through the midpoint of it

I got this question by my school principal while I was bunking the class.

This interesting question is from Loci of Points by Different Methods topic in chapter Loci of Points & Orthographic Projections of Engineering Drawing

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Correct option is (a) an ellipse

Explanation: The two points given are foci of ellipse. Ellipse is a curve whose eccentricity is less than one. The process given is one of the methods to draw an ellipse in an easy way. Since the sum of distances from two fixed points to point P on curve is always constant.

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