Question

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Answer 1

Answer: C. Outside the circle.

Step-by-step explanation:

To find whether point M lies on the circle, first derive the equation of the circle from the radius and center given.

Equation of a circle:

$(x-h)^2 + (y-k)^2=r^2$

Substitute the coordinates (0, 0) for h and k, and 2 times the square root of 3 for r:

$x^2 + y^2 = 12$

Now, substitute the points (-3, 2) for x and y:

$9 + 4 = 12$

This equation is incorrect, as the (x, y) coordinates produce a greater value than the radius of the circle squared. When this occurs, the point given is outside of the circle.

(A point like (1, 1), when substituted into the equation and solved to get 1 + 1 = 12, would be inside the circle, as its (x, y) coordinates produce a smaller value than the radius of the circle squared.)

As such, the correct answer is C.