Circle Equations and Properties

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 a circle given by the equation (x - 2)² + (y + 3)² = 16?

Back

Center: (2, -3)

Front

What is the radius of a circle with the equation (x + 1)² + (y - 4)² = 36?

Back

Radius = 6 units

Front

How do you determine if a point (x₁, y₁) is inside, outside, or on a circle with equation (x - h)² + (y - k)² = r²?

Back

Calculate the distance from (x₁, y₁) to (h, k). If d < r, inside; d = r, on; d > r, outside.

Front

What is the equation of a circle with radius 5 and center (0, 0)?

Back

x² + y² = 25

Front

What is the center and radius of the circle given by the equation (x - 5)² + (y + 2)² = 49?

Back

Center: (5, -2), Radius = 7 units

Front

What does the term 'h' represent in the standard circle equation (x - h)² + (y - k)² = r²?

Back

The x-coordinate of the center of the circle.

Front

What does the term 'k' represent in the standard circle equation (x - h)² + (y - k)² = r²?

Back

The y-coordinate of the center of the circle.

Front

If a circle has the equation x² + y² = 16, what is its radius?

Back

Radius = 4 units

Front

What is the equation of a circle with center (-3, 4) and radius 2?

Back

(x + 3)² + (y - 4)² = 4