Acircle that is centered at the origin contains the point (0,4). how can you prove or disprove that the point (2,
6
) also lies on the circle? does the point (2,
6
) lie on the circle?

If the circle is at the origin and (0,4) is a point on the circle then the radius of the circle is:

r^2=0^2+4^2

r^2=16

r=4

so we can check that the other point is four units from the origin and thus also on the circle...

d^2=2^2+6^2

d^2=4+36

d^2=40

since d^2>r^2, (2,6) is outside the circle...