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

Step-by-step 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:

$(x-5)^2+(y+3)^2=25\\(-2-5)^2+(4+3)^2=25\\(-7)^2+(7)^2=25\\98\neq25$

Therefore, as $98\neq25$ then the point is not on the circle.

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

$(x-5)^2+(y+3)^2$

$98>25$ 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.