Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).

To Find: Relation between x and y
Given: (x, y) is equidistant from (3, 6) and (-3, 4)
From the figure it can be seen that Point (x, y) is equidistant from (3, 6) and (- 3, 4)
This means that the distance of (x, y) from (3, 6) will  be equal to distance of (x, y) from (- 3, 4)
We know by distance formula that, distance between two points A(x1, y1), B(x2, y2) is given by

Therefore,

√[(x- 3)2 + (y - 6)2] = √[(x + 3)2 + (y- 4)2]

Squaring both sides, we get

(x – 3)2 + (y – 6)2 = (x + 3)2 + (y – 4)2

x2 + 9 – 6x + y2 + 36 – 12y = x2 + 9 + 6x + y2 + 16 – 8y

36 – 16 = 6x + 6x + 12y – 8y

20 = 12x + 4y

3x + y = 5

3x + y – 5 = 0 is the relation between x and y

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