Question

Find the abscissa of point whose coordinate is 4 and which are at a distance of 5 units from(5,0).

Answer 1

let the coordinates of required point be (x,4)
distance=5
$\sqrt{( {x - 5)}^{2} + ( {4 - 0)}^{2} } = 5 \\ squaring \\ {(x - 5)}^{2} + 16 = 25 \\ {(x - 5)}^{2} = 25 - 16 \\ {(x - 5)}^{2} = 9 \\ x - 5 = 3 \: \: \: \: \: \: or \: \: \: \: \: \: x - 5 = - 3 \\ x = 8 \: \: \: \: \: \: \: \: \: \: \: \: \: or \: \: \: \: x = 5 - 3 = 2 \\ \\ required \: coordinates \: are$
(8,4) or (2,4)