Equation of a Circle

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 is the center of the circle in the equation (x - 4)² + (y + 3)² = 25?

Back

(4, -3)

Front

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

Back

6

Front

How do you find the distance between the center of a circle and a point outside the circle?

Back

Use the distance formula: d = √((x2 - x1)² + (y2 - y1)²) where (x1, y1) is the center and (x2, y2) is the point.

Front

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

Back

The distance from the center to the point is less than the radius.

Front

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

Back

The distance from the center to the point is equal to the radius.

Front

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

Back

The distance from the center to the point is greater than the radius.

Front

If a circle has a center at (0, 0) and a radius of 5, what is its equation?

Back

x² + y² = 25

Front

What is the diameter of a circle?

Back

The diameter is twice the radius.

Front

In the equation (x - 1)² + (y + 2)² = 9, what is the radius?

Back

3