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Question
Find the coordinates of the points on the y-axis, which are at a distance of 10 units from the point (-8, 4).
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Solution
Let the coordinates of the point on y-axis be (0, y).
From the given information, we have:
`sqrt((0 + 8)^2 + (y - 4)^2)` = 10
(0 + 8)2 + (y - 4)2 = 100
64 + y2 + 16 - 8y = 100
y2 - 8y - 20 = 0
y2 - 10y + 2y - 20 = 0
y(y - 10) + 2(y - 10) = 0
(y - 10)(y + 2) = 0
y = 10, - 2
Thus, the required co-ordinates of the points on y-axis are (0, 10) and (0, -2).
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