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A circle has its center at (5,-3) and contains the point (8,-3). Which of the points is also on the circle?

User Saltymule
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Final answer:

Using the center (5,-3) and a point on the circle (8,-3), the radius is found to be 3 units. Thus, any point 3 units away from the center and on the same y-coordinate is also on the circumference of the circle.

Step-by-step explanation:

To determine which point is also located at the circumference of the circle, we need to use the center and a point on the circle to find the radius. The center is given as (5,-3), and the point on the circle is (8,-3). Calculating the distance between these two points will give us the radius, which is the distance in the x-axis (horizontal line) and is 8 - 5 = 3 units. Since the radius is the same all around the circle, any point that is 3 units away from the center in any direction is on the circumference. If a point shares the same y-coordinate as the center, as in this case, it will be 3 units to the left or right of the center to be on the circle.

As for the foci of a circle, it's important to clarify that unlike an ellipse that has two distinct foci, a circle has a single focus which coincides with the center of the circle. Therefore, all foci-related options presented are incorrect for a circle since they reference an ellipse or misunderstand the nature of a circle's focus.

User Martin Melka
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