Question
Find a point on the $y-$axis which is equidistant from the points $(5, 2)$ and $(-4, 3).$
✓
Answer
Let the co$-$ordinates of the required point on $y-$axis be $P (0, y).$
The given points are $A (5, 2)$ and $B (-4, 3).$
Given$, \text{PA} =\text{PB}$
$PA^2 = PB^2$
$(0 -5)^2 + (y -2)^2 = (0 + 4)^2 + (y - 3)^2$
$25 + y^2 + 4 - 4y = 16 + y^2 + 9 - 6y$
$2y = -4$
$y = -2$
Thus, the required point is $(0, -2).$
The given points are $A (5, 2)$ and $B (-4, 3).$
Given$, \text{PA} =\text{PB}$
$PA^2 = PB^2$
$(0 -5)^2 + (y -2)^2 = (0 + 4)^2 + (y - 3)^2$
$25 + y^2 + 4 - 4y = 16 + y^2 + 9 - 6y$
$2y = -4$
$y = -2$
Thus, the required point is $(0, -2).$
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