Graphing Circles

Front

What is the standard equation of a circle?

Back

(x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

What does (h, k) represent in the circle equation?

Back

(h, k) is the center of the circle.

Front

If the center of a circle is at (2, -3) and the radius is 5, what is the equation?

Back

(x - 2)² + (y + 3)² = 25.

Front

How do you find the radius from the equation of a circle?

Back

The radius is the square root of the number on the right side of the equation (r²).

Front

What is the center of the circle in the equation (x + 4)² + (y - 1)² = 36?

Back

The center is (-4, 1).

Front

What does the radius of a circle determine?

Back

The distance from the center to any point on the circle.

Front

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

Back

The radius is 3 (since √9 = 3).

Front

What is the relationship between the radius and the area of a circle?

Back

Area = πr², where r is the radius.

Front

If a circle has a radius of 4, what is the area?

Back

Area = π(4)² = 16π.

Front

How do you graph a circle given its equation?

Back

Identify the center (h, k) and plot points at a distance r from the center in all directions.