Question

what is the diameter of this circle?

Explanation:

Step1: Identify the center and a point on the circle

The center of the circle (let's call it \( C \)) appears to be at \( (-6, 4) \) (by looking at the grid). A point on the circle (let's take the rightmost point) is at \( (0, 4) \) (since it lies on the line \( y = 4 \) and the circle intersects the \( y \)-axis there).

Step2: Calculate the distance between the center and the point (radius)

Using the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \), but since \( y_1 = y_2 = 4 \), the distance (radius \( r \)) is just the absolute difference of the \( x \)-coordinates: \( |0 - (-6)| = 6 \).

Step3: Calculate the diameter

The diameter \( d \) of a circle is twice the radius, so \( d = 2r \). Substituting \( r = 6 \), we get \( d = 2\times6 = 12 \).

Answer:

12