Question

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

(3, 2)

Answer 1

exterior

Explanation:

You want to know if (3, 2) is an interior or exterior point of the circle defined by (x -5)² +(y +3)² = 25.

Distance from center

We can find the square of the distance of the point from the center of the circle using the equation for the circle.

(x -5)² +(y +3)² = r²

(3 -5)² +(2 +3)² = 4 +25 = 29 > 25 . . . . use (x, y) = (3, 2) in the equation

The point is farther away from the center than points that are on the circle. The point (3, 2) is an exterior point.