Question

Find the point on y axis which is equidistant from the points (5,-2) and (-3,2).
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Answer 1

Since the point is on y-axis it's coordinates are (0,y).

If P(0,y) be the point equidistant from A(5,-2) and B(-3,2),

AP=BP Given

AP2=BP2 squaring as to remove roots.

(0-5)2+(y+2)2=

(-3-0)2+(2-y)2

=25+y2+4y+4=9+4-4y+y2

=16= -8y

So,y= -2.