Question

Find the point on x-axis which is equidistant from the points (2,-2) and (-4,2)
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Answer 1

Answer:

$x = - 1$

Step-by-step explanation:

Let p (x, o) be a point on x-axis

$pa = pb \\ \\ pa {}^{2} = pb {}^{2} \\ \\ (x - 2) {}^{2} + (0 + 2) { }^{2} = (x + 4) + (0 - 2) {}^{2} \\ \\ x {}^{2} + 4 - 4 \times 4 \\ \\ = x {}^{2} + 16 + 8x + 4 \\ - 4 \times \: + 4 = 8 \times \: + 16 \\ x = - 1$

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Answer 2

Answer:

Let P(x,0) be a point on X-axis PA = PB PA2 = PB2 (x - 2)2 + (0 + 2)2 = (x + 4)2 + (0 - 2)2 x2 + 4 - 4x + 4 = x2 + 16 + 8x + 4 -4x + 4 = 8x + 16 x = -1 P(-1,0)