Answer :

(i) Distance between two points =

Here the second point is origin.


5 =


Squaring on both sides,


25 = 16 + y2


Or y = + 3 or - 3.


(ii) A point on y-axis will have x coordinate 0.


So, let the point on y-axis be (0, y) .


If this point is equidistant from given two points,


=


Squaring on both sides,


(y - 3) 2 + 4 = (y - 2) 2 + 1


Or y2 - 3y + 9 + 4 = y2 - 2y + 4 + 1


13 - 5 = y


y = 8


So the coordinate on the y-axis is (0, 8)


(iii) Let the point on x-axis be A (x, 0)


Let the point on y-axis be B (0, y)


To satisfy the conditions given in the problem,


The distance of A from origin should be the same as the distance of B from origin.


The distance between two points =



Or x= + y or x = - y


The coordinates should be (0, x) and (x, 0) where x is any real number.


(iv) (x, 0) and (- x, 0)


(v) (0, y) and (0, - y)


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