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

Question

asked Oct 24, 2020 133k views

1 Answer

Codigo Morsa · Answer 1 · 2020-10-30T22:06:57+0000

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.