Q. 164.4( 21 Votes )

# Short answer type

Answer :

(i) Distance between two points =

Here the second point is origin.

5 =

Squaring on both sides,

25 = 16 + y^{2}

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 y^{2} - 3y + 9 + 4 = y^{2} - 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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