Question

A point moves in such a way that the sum of square of its distance from the points $A(2,0)$ and$B( - 2,0)$ is always equal to the square of the distance between A and B. The locus of the point is.

• A. $x^{2} + y^{2} - 2 = 0$
• B. $x^{2} + y^{2} + 2 = 0$
• C. $x^{2} + y^{2} + 4 = 0$
• D. $x^{2} + y^{2} - 4 = 0$

Answer 1

Answer: (D)

$x^{2} + y^{2} - 4 = 0$

Answer 2

$( x - 2 ) ^ { 2 } + y ^ { 2 } + ( x + 2 ) ^ { 2 } + y ^ { 2 } = 16 \Rightarrow x ^ { 2 } + y ^ { 2 } = 4$.