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

Step-by-step explanation:

equation of a circle is (x - a)² + (y - b)² = r²

where a is the x-coordinate in centre of circle, b is is y-coordinate in centre of circle and r is the radius of the circle (half of diameter).

if our circle lies on the y-axis then its x-coordinate must be 0.

just x², no ( x - a)².

if its diameter is 12, then its radius is 6.

in formula, r² must me 6² = 36.

only the first and last equations in the questions match this criteria.

that is, x² + (y - 3)² = 36, and x² + (y +8)² = 36.