Question

The equation $\sqrt{x^2+y^2}+\sqrt{(x-3{)}^2+(y-4{)}^2}=6$ represents

• A. a parabola
• B. a hyperbola
• C. an ellipse
• D. a line segment

Answer 1

The correct option is C an ellipse

$\sqrt{x^2+y^2}+\sqrt{(x-3{)}^2+(y-4{)}^2}=6$
Equation (1) represents the locus of point P (x,y) whose sum of distances from points $O(0,0)$ and $A(3,4)$ is constant (=6). The constant is greater than the distance between points $O$ and $A(=5)$.
Hence, the locus of $P$ is an ellipse.