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Sav [38]
2 years ago
7

Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis

Mathematics
1 answer:
Tju [1.3M]2 years ago
8 0

The equations representing the circle having a diameter of 12 units and a center lying on y-axis are <u>x² + (y – 3)² = 36</u>, and <u>x² + (y + 8)² = 36</u>, making <u>options 1, and 5</u> the two choices.

In the question, we are looking for the equations of the circle having a diameter of 12 units and a center lying on y-axis.

The standard form of the equation of a circle is (x - h)² + (y - k)² + r², where (h, k) is the center of the circle, and r is its radius.

A circle having a diameter of 12 units, will have a radius of 12/2 = 6 units. Thus, r = 6.

A circle having the center on the y-axis will have a center as (0, k) as all points on the y-axis have x-coordinate 0.

Thus, the equation of the circle, with a diameter of 12 units and the center lying on the y-axis takes the form:

x² + (y - k)² = 6², or, x² + (y - k)² = 36.

From the given options, the equations <u>x² + (y – 3)² = 36</u>, and <u>x² + (y + 8)² = 36</u>, are of this form.

Thus, the equations representing the circle having a diameter of 12 units and a center lying on y-axis are <u>x² + (y – 3)² = 36</u>, and <u>x² + (y + 8)² = 36</u>, making <u>options 1, and 5</u> the two choices.

Learn more about equations of circle at

brainly.com/question/16039879

#SPJ4

The provided question is incomplete. The complete question is:

"Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.

  1. x² + (y – 3)² = 36
  2. x² + (y – 5)² = 6
  3. (x – 4)² + y² = 36
  4. (x + 6)² + y² = 144
  5. x² + (y + 8)² = 36."
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