Q. 12 A4.7( 4 Votes )

# If the distances of P(x, y) from points A(3, 6) and B(- 3, 4) are equal, prove that 3x + y = 5

Given points are A(3, 6) and B(- 3, 4). It is told that S(x, y) is equidistant from A and B. So, we get SA = SB,

We know that distance between two points (x1, y1) and (x2, y2) is .

Now,

SA = SB

SA2 = SB2

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

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

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

12x + 4y = 20

3x + y = 5

Thus proved.

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