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

x² + (y – 3)² = 36

and

x²+ (y + 8)²= 36

Explanation:

The equation of circle that has a center (a, b) is given by the formula

(x - a)² + (x - b)² = r²

where r is the radius of the circle

If the circle lies on the y axis, its x-coordinate must be 0.
The radius of the circle = 1/2 x diameter = 1/2 x 12 = 6 units

So the equation must be of the form
(x - 0)² + (y - b)² = 36

We can eliminate x² + (y – 5)² = 6
We can also eliminate (x + 6)² + y² = 144

That leaves us with the two possible equations

x² + (y – 3)² = 36 (center at 0, 3)

and

x²+ (y + 8)²= 36 (center at (0, -8) )