one way would be to find the distance from the point to the center of the circle and compare it to the radius
for
[tex](x-h)^2+(y-k)^2=r^2[/tex]
the center is (h,k) and the radius is r
and the distance formula is
distance between [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is
[tex]D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
r=radius
D=distance form (8,4) to center
if r>D, then (8,4) is inside the circle
if r=D, then (8,4) is on the circle
if r<D, then (8,4) is outside the circle
so
[tex](x+2)^2+(y-3)^2=18[/tex]
[tex](x-(-2))^2+(y-3)^2=(\sqrt{18})^2[/tex]
[tex](x-(-2))^2+(y-3)^2=(3\sqrt{2})^2[/tex]
the radius is [tex]3\sqrt{2}[/tex]
center is (-2,3)
find distance between (8,4) and (-2,3)
[tex]D=\sqrt{(8-(-2))^2+(4-3)^2}[/tex]
[tex]D=\sqrt{(8+2)^2+(1)^2}[/tex]
[tex]D=\sqrt{10^2+1}[/tex]
[tex]D=\sqrt{100+1}[/tex]
[tex]D=\sqrt{101}[/tex]
[tex]r=3\sqrt{2}[/tex]≈4.2
[tex]D=\sqrt{101}[/tex]≈10.04
do r<D
(8,4) is outside the circle
