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As given
The point on Y-axis which are at a distance of 5√2 units from the point (5,8) .
As the point on Y-axis is in the form (0, y) .
Thus put all the values in the formula
As (√2 )² = 2
Put in the above
25*2 =25+(y-8)^{2}
(As (a - b)² = a² + b² - 2ab )
50 = 25 + y² + 64 - 2 × y × 8
50 = 25 + y² + 64 - 16y
= y² - 16y + 89 - 50
= y² - 16y + 39
= y² - 13y - 3y + 39
= y (y - 13) -3 (y - 13)
= (y- 13)(y-3)
y = 13 , y = 3
Therefore the value of y are 13 and 3 .