A.maths .locus...

Let the coordinates of P be (x, y)
| PA -PB | =2
|√{(y - 0)² + [y -(-3)]² } - √{(y - 0)² + (y - 3)² } | = 2
|√[y² + (x + 3)²] - √[y² + (x - 3)²] | = 2
{|√[y² + (x + 3)²] - √[y² + (x - 3)²] | }² = 2²
{[y²+ (x + 3)²]}² - 2{√[y² + (x + 3)²]}{√[y² + (x - 3)²]} + {√[y² + (x - 3)²]}² = 4 y² + (x + 3)² - 2{√[y² + (x + 3)²]}{√[y² + (x - 3)²]} + [y² + (x - 3)²] = 4
- 2{√[y² + (x + 3)²]}{√[y² + (x - 3)²]} + 2y² + 2x² + 18 = 4
√{ [y² + (x + 3)²][y² + (x - 3)²] } = y² + x² + 7
{√{ [y² + (x + 3)²][y² + (x - 3)²] } }² = (y² + x² + 7)²
[y² + (x + 3)²][y² + (x - 3)²] = (y² + x² + 7)²
y4 + y²(x - 3)² + y²(x + 3)² + (x + 3)²(x - 3)² = (y² + x² + 7)²
y4 + y²(x² - 6x + 9) + y²(x² + 6x + 9) + (x² + 6x + 9)(x² - 6x + 9) = (y² + x² + 7)²
y4 + 2x²y² + 18y² + x4 - 6x³ + 9x² + 6x³ -36x² + 54x + 9x² - 54x + 81 = y4 + x²y² + 7y² +x²y² + x4 + 7x² + 7y² + 7x² + 49
18y² - 18x² + 81 = 14y² + 14x² + 49
32x² - 4y² -32 = 0
8x² - y² = 8
therefore, the equation of the locus of P is: 8x² - y² = 8

ans= 8x^2-8=y^2