The equation which represents the circle is x²+(y-3)²=36. The correct option is A.
Given that the circle have diameter 12 units and a center that lies on the y-axis.
A circle is a closed curve drawn from a fixed point called the center, and all points on the curve are equidistant from the midpoint of the center.
The standard form for finding the equation of a circle is expressed in the form is
(x-a)²+(y-b)²=r² ......(1)
Where (a,b) is the center and r is the radius.
Given that the diameter is 12.
So, the radius is 12/2=6
It is also given that center lies on the y-axis therefore the center will be (0,3).
Now, we will substitute these values in equation (1), we get
(x-0)²+(y-3)²=6²
x²+(y-3)²=36
Hence, the equation which represents the circle with diameter 12 units and center lies on the y-axis is x²+(y-3)²=36.
Learn more about the equation of circle from here brainly.com/question/24810873
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