Question

The coordinates of the points A and B are (a, 0) and $( - a,0)$ respectively. If a point P moves so that $PA^{2} - PB^{2} = 2k^{2}$, when k is constant, then the equation to the locus of the point P , is.

• A. $2ax - k^{2} = 0$
• B. $2ax + k^{2} = 0$
• C. $2ay - k^{2} = 0$
• D. $2ay + k^{2} = 0$

Answer 1

Answer: (B)

$2ax + k^{2} = 0$

Answer 2

Let the point be (x, y),

Then $( x - a ) ^ { 2 } + y ^ { 2 } - ( x + a ) ^ { 2 } - y ^ { 2 } = 2 k ^ { 2 }$

$\Rightarrow - 4 a x - 2 k ^ { 2 } = 0 \Rightarrow 2 a x + k ^ { 2 } = 0$.