Question

Find the point on the y-axis which is equidistant from the point 5, - 2 and minus 3, 2

Answer 1

Let the point of x-axis be P(x, 0)
Given A(2, -50) and B(-2, 9) are equidistant from P
That is PA = PB
Hence PA2 = PB2  → (1)
Distance between two points is √[(x2 - x1)2+ (y2 - y1)2]
PA = √[(2 - x)2 + (-50 - 0)2]
PA2 = 4 - 4x +x2 + 2500 = x2- 4x + 2504
Similarly, PB2 = x2 + 4x + 85
Equation (1) becomes
x2 - 4x + 2504 = x2 + 4x + 85
- 8x = 2419
x = -2419/8
Hence the point on x-axis is (-7, 0)