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

The equations for circles of a diameter of 12 units and centered on the y-axis are:

• x^2 + (y - 3)^2 = 36
• x^2 + (y + 8)^2 = 36

Which is the equation of the circle?

For a circle of radius R, centered at the point (a, b), the general equation is:

(x - a)^2 + (y - b)^2 = R^2

so if we want a circle centered on the y-axis, we need to have x = 0, then:

x^2 + (y - b)^2  = R^2

And we also know that the diamter is 12 units, then the radius is half of that:

R = 12/2 = 6 units

Then the circle equation is:

x^2 + (y - b)^2 = 6^2

x^2 + (y - b)^2 = 36

Of the given options the only ones that have this form is the first one:

x^2 + (y - 3)^2 = 36

And the last one:

x^2 + (y + 8)^2 = 36

Learn more about circles:

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