Answer:
inside
Explanation:
You want to know where the point (3, -2) lies in relation to the circle defined by (x -1)² +(y +2)² = 16.
Substitution
Using the point values for x and y will tell you the answer. The expression in x and y will tell you the square of the distance from the center to the point (x, y).
(3 -1)² +(-2 +2)² = 2² +0 = 4
We observe that 4 < 16, so the distance from the center to the given point is less than the radius, so the point lies inside the circle.
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Additional comment
The circle centered at (h, k) with radius r had equation ...
(x -h)² +(y -k)² = r²
The value 4, above, tells us the point would lie on a circle of radius √4 = 2 with the same center. That is inside the given circle with radius 4.
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