Answer:
Explanation:
To determine whether the point (2, √3) lies on the circle centered at the origin and contains the point (-3, 0), we can calculate the distance between the center of the circle and the given point. If the distance is equal to the radius of the circle, then the point lies on the circle.
The center of the circle is the origin (0, 0), and the given point is (2, √3). To calculate the distance, we can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates, we have:
Distance = √((2 - 0)^2 + (√3 - 0)^2)
= √(4 + 3)
= √7
The distance between the center of the circle and the point (2, √3) is √7.
Now, let's consider the radius of the circle. The radius is the distance between the center of the circle and any point on the circle. In this case, the radius is the distance between the origin (0, 0) and the point (-3, 0).
Radius = √((-3 - 0)^2 + (0 - 0)^2)
= √(9 + 0)
= √9
= 3
Since the distance between the center of the circle and the point (2, √3) is not equal to the radius of the circle, which is 3, we can conclude that the point (2, √3) does not lie on the circle that is centered at the origin and contains the point (-3, 0).
Therefore, the statement is disproven.