Question

Is the given point interior , exterior, or on the circle k (x+2)2 + (y-3)2 =18 P (8,4)

Answer 1

one way would be to find the distance from the point to the center of the circle and compare it to the radius

for

`(x-h)^2+(y-k)^2=r^2`
the center is (h,k) and the radius is r

and the distance formula is
distance between
`(x_1,y_1)` and
`(x_2,y_2)` is

`D=√((x_1-x_2)^2+(y_1-y_2)^2)`


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

`(x+2)^2+(y-3)^2=18`

`(x-(-2))^2+(y-3)^2=(√(18))^2`

`(x-(-2))^2+(y-3)^2=(3√(2))^2`

the radius is
`3√(2)`
center is (-2,3)

find distance between (8,4) and (-2,3)


`D=√((8-(-2))^2+(4-3)^2)`

`D=√((8+2)^2+(1)^2)`

`D=√(10^2+1)`

`D=√(100+1)`

`D=√(101)`





`r=3√(2)`≈4.2

`D=√(101)`≈10.04

do r<D

(8,4) is outside the circle