Q. 104.2( 309 Votes )

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

Answer :

**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(x_{1, }y_{1}), B(x_{2}, y_{2}) 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}

x^{2} + 9 – 6x + y^{2} + 36 – 12y = x^{2} + 9 + 6x + y^{2} + 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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