Question

circle has a diameter of 12 units, and its center lies on the x-axis. What could be the equation of the circle? Check all that apply.

(x – 12)2 + y2 = 12
(x – 6)² + y² = 36
x² + y² = 12
x² + y² = 144
(x + 6)² + y² = 36
(x + 12)² + y² = 144

Answer 1

Answer:

2) (x – 6)² + y² = 36

5) (x + 6)² + y² = 36

Step-by-step explanation:

Answer 2

The possible equation of a circle with diameter of 12 units, and its center lies on the x-axis is (x – 6)² + y² = 36 and (x + 6)² + y² = 36.

The standard circle equation

The standard equation of a circle is given by:

(x - h)² + (y - k)² = r²

Where (h, k) is the circle center, r is the radius.

Since the diameter is 12, hence r = 12/2 = 6

The circle center is on the x axis (h, 0). The circle equation is in the form:

(x - h)² + y² = 6²

The possible equation of a circle with diameter of 12 units, and its center lies on the x-axis is (x – 6)² + y² = 36 and (x + 6)² + y² = 36.

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