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

What are the coordinates of the center of the circle given by the equation (x - 2)² + (y + 3)² = 16?

Back

Center: (2, -3)

Front

How do you determine the radius of a circle from its equation (x - 5)² + (y - 1)² = 36?

Back

Radius = √36 = 6 units

Front

What is the radius of a circle with the equation x² + y² = 25?

Back

Radius = √25 = 5 units

Front

If a circle has the equation (x + 4)² + (y - 2)² = 9, what is the center and radius?

Back

Center: (-4, 2), Radius: 3 units

Front

What does it mean for a point to be 'inside' a circle?

Back

A point (x, y) is inside a circle if (x - h)² + (y - k)² < r², where (h, k) is the center and r is the radius.

Front

What does it mean for a point to be 'on' a circle?

Back

A point (x, y) is on a circle if (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

What does it mean for a point to be 'outside' a circle?

Back

A point (x, y) is outside a circle if (x - h)² + (y - k)² > r², where (h, k) is the center and r is the radius.

Front

Write the equation of a circle with center (0, 0) and radius 10.

Back

x² + y² = 100

Front

What is the center and radius of the circle given by the equation (x - 1)² + (y + 4)² = 49?

Back

Center: (1, -4), Radius: 7 units