Question

Select interior, exterior, or on the circle (x - 5) 2 + (y + 3) 2 = 25 for the following point. (-2, 4)

Answer 1

Answer: Exterior

Explanation:

Substitute the point (-2,4) into the equation of the circle
`(x-5)^2+(y+3)^2=25`.

Knowing that:

`x=-2\\y=4`

Then:

`(x-5)^2+(y+3)^2=25\\(-2-5)^2+(4+3)^2=25\\(-7)^2+(7)^2=25\\98\\eq25`

Therefore, as
`98\\eq25` then the point is not on the circle.

If a point is in the interior of the circle , then:

`(x-5)^2+(y+3)^2<25`

`98>25` Then the point (-2,4) is not in the interior of the circle.

If a point is in the exterior of the circle, then:

`(x-5)^2+(y+3)^2>25`

`98>25` Then the point (-2,4) is in the exterior of the circle.