Question
If P(x, y) is equidistant from the points A(7, 1) and B(3, 5), find the relation between x and y.
✓
Answer
Let the point P(x, y) be equidistant from the points A(7, 1) and B(3, 5).
Then,
$PA = PB$
$\Rightarrow PA^2 = PB^2$
$\Rightarrow (x- 7)^2 + (y - 1)^2= (x - 3)^2 + (y - 5)^2$
$\Rightarrow x^2 + y^2 - 14x - 2y + 50 = x^2 + y^2 - 6x - 10y + 34$
$\Rightarrow 8x - 8y = 16$
$\Rightarrow x - y = 2$
Then,
$PA = PB$
$\Rightarrow PA^2 = PB^2$
$\Rightarrow (x- 7)^2 + (y - 1)^2= (x - 3)^2 + (y - 5)^2$
$\Rightarrow x^2 + y^2 - 14x - 2y + 50 = x^2 + y^2 - 6x - 10y + 34$
$\Rightarrow 8x - 8y = 16$
$\Rightarrow x - y = 2$
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