SAT® Math Practice Tests and Questions - Free Printable

To find the equation of the circle graphed in the xy-plane, we need to recall the standard form of a circle’s equation:

> (x – h)² + (y – k)² = r²

Where:
- (h, k) is the center of the circle
- r is the radius

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Step 1: Find the center (h, k)

Looking at the graph:

- The circle appears to be centered at x = 3, y = -4
- Horizontally, the circle is symmetric about x = 3 (midpoint between leftmost point at x=1 and rightmost at x=5)
- Vertically, it's symmetric about y = -4 (midpoint between top at y=0 and bottom at y=-8)

✔ So, center = (3, -4) → meaning h = 3, k = -4

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Step 2: Find the radius r

From the center (3, -4), measure the distance to any point on the circle.

Let’s go from center (3, -4) to the top point of the circle: (3, 0)

Vertical distance = |0 – (-4)| = 4 → so radius = 4

Alternatively, to the rightmost point: (7, -4)

Horizontal distance = |7 – 3| = 4 → same radius.

✔ So, r = 4 → r² = 16

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Step 3: Plug into standard form

Using (h, k) = (3, -4), r² = 16:

> (x – 3)² + (y – (-4))² = 16
> → (x – 3)² + (y + 4)² = 16

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Step 4: Match with options

A. (x + 3)² + (y – 4)² = 4 → center (-3, 4), radius 2 ✘
B. (x – 3)² + (y + 4)² = 16 → center (3, -4), radius 4 ✔
C. (x + 3)² + (y – 4)² = 16 → center (-3, 4), radius 4 ✘

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✔ Final Answer: B. (x – 3)² + (y + 4)² = 16