Question 1011877
{{{x^2 +y^2 = 16}}}

if you compare it to standard equation

{{{(x-h)^2 +(y-k)^2 = r^2}}}

you see that your circle is a circle with center at origin and radius {{{r=4}}}; so x-intercepts are at {{{x=-4}}} and {{{x=4}}}

if {{{A}}}  is a point where the circle  cuts the {{{x}}} axis,  it must be radius length distance from the center or where the x-intercepts are which means could be only at ({{{-4}}},{{{0}}}) or at ({{{4}}},{{{0}}})

{{{drawing( 600, 600, -5, 5, -5, 5,
circle(-4,0,0.12),circle(4,0,0.12),locate(-4,0.4,A(-4,0)),locate(4,0.4,A(4,0)),
green(circle(0,0,4)),
 graph( 600, 600, -5, 5, -5, 5,-sqrt(-x^2+16), sqrt(-x^2+16))) }}}