Circle Equations

Front

What is the standard equation of a circle with center (h, k) and radius r?

Back

(x - h)² + (y - k)² = r²

Front

Write the equation of a circle with center (0, 0) and radius 5.

Back

x² + y² = 25

Front

What does the center of a circle represent in its equation?

Back

The center (h, k) is the point from which all points on the circle are equidistant.

Front

How do you determine if a point (x, y) is inside, outside, or on a circle given by the equation (x - h)² + (y - k)² = r²?

Back

Calculate the distance from the point to the center. If d < r, it's inside; if d = r, it's on; if d > r, it's outside.

Front

Write the equation of a circle with center (2, -3) and radius 4.

Back

(x - 2)² + (y + 3)² = 16

Front

What is the radius of a circle if its equation is (x + 1)² + (y - 2)² = 36?

Back

The radius is 6 units.

Front

Identify the center and radius of the circle given by the equation (x - 5)² + (y + 1)² = 49.

Back

Center: (5, -1), Radius: 7 units.

Front

Write the equation of a circle with center (-3, 4) and radius 2.

Back

(x + 3)² + (y - 4)² = 4

Front

What is the distance formula used to find the distance between two points (x₁, y₁) and (x₂, y₂)?

Back

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Front

Write the equation of a circle with center (1, 1) and radius 1.

Back

(x - 1)² + (y - 1)² = 1