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A point on the y-axis which is equidistant from the points A(6, 5) and B(-4, 3) is:

Solution

Correct Option: 1

Let P(0,y)P(0,y). Then PA2=PB2PA^2 = PB^2:

36+(y5)2=16+(y3)236 + (y-5)^2 = 16 + (y-3)^2.

36+y210y+25=16+y26y+936 + y^2 - 10y + 25 = 16 + y^2 - 6y + 9.

6110y=256y4y=36y=961 - 10y = 25 - 6y \Rightarrow 4y = 36 \Rightarrow y = 9.

Point is (0,9)(0, 9).

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