Question

The locus of a point which moves such that the sum of its distances from two fixed points is a constant is

• A. A circle
• B. A parabola
• C. An ellipse
• D. A hyperbola

Answer 1

Answer: (C)

An ellipse

Let $(x,y)$ be locus of a moving point and $(p,q),(r,s)$ be two fixed points

Distance of $(x,y)$ from $(p,q)$ is $\sqrt{{(x-p)}^2+{(y-q)}^2}$

Distance of $(x,y)$ from $(r,s)$ is $\sqrt{{(x-r)}^2+{(y-s)}^2}$

Sum of its distances is $\sqrt{{(x-p)}^2+{(y-q)}^2}+\sqrt{{(x-r)}^2+{(y-s)}^2}=c$

An ellipse is a curve in a plane surrounding two focal points such that the sum of the distances of two focal points is constant for every point on the curve.

Solving above equation, we get an ellipse