Question

Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36

Answer 1

(a) x² +(y -3)² = 36

(e) x² +(y +8)² = 36

Explanation:

You want to identify the equations for a circle with center on the y-axis and diameter 12 units.

Circle equation

The equation of a circle with center (h, k) and radius r is ...

(x -h)² +(y -k)² = r²

Application

If the center is on the y-axis, then h = 0. If the diameter is 12 units, then the radius is 6 units and r² = 36. This means the desired equation will be of the form ...

(x -0)² +(y -k)² = 36

x² +(y -k)² = 36 . . . . . . . for some value of k

The relevant answer choices have k = 3 or -8:

x² +(y -3)² = 36

x² +(y +8)² = 36

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