Answers

2015-02-04T20:16:28+05:30
Let the point be Y(0,y)
using the distance formula,
 \sqrt{16+(7-y)^{2} } =2 \sqrt{5}  \\ 16+(7-y) ^{2} =20  \\ (7-y) ^{2} =4 \\ 7-y=2 \\ y=5
so the coordinates are Y(0,5)
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2015-02-06T12:47:39+05:30
Point on Y axis be P(0, y)
Distance between two points =  \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
 \sqrt{(-4-0)^2 + (7-y)^2} = 2\sqrt{5} 
 \sqrt{16 + (7-y)^2} = 2\sqrt{5} 
Squaring on both sides
16 +  (7 - y)² = 20
⇒ (7 - y)² = 4
7 - y = \pm 2
7 - y = 2      and      7 - y = - 2

y = 5       and y = 9

The points are  (0,5) and (0, 9)

So, there are two points. 
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