Question

Find the coordinates of the sides on the x axis which are at distance of 10 units from the points -4,8

Answer 1

let the point on x axis =(x, 0)

distance from (-4,8)=10
$\sqrt{ {(x + 4)}^{2} + 8 {}^{2} } = 10 \\ sq \: both \: sides \\ (x + 4) {}^{2} = 100 - 64 \\ (x + 4) {}^{2} = 36 \\ x + 4 = 6 \: or \: x + 4 = - 6 \\ x = 2 \: or \: x = - 10 \\ so \: x = 2$
because length can't be negative.....
hence x=2
......

hence point is (2,0)