Graphing Circles on a coordinate plane

Front

What is the standard form of a circle's equation?

Back

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

Front

What do the variables h and k represent in the circle equation?

Back

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

Front

How do you find the radius from the circle equation?

Back

The radius is the square root of the number on the right side of the equation (r = √value).

Front

What is the center of the circle in the equation (x - 2)² + (y + 3)² = 16?

Back

Center is (2, -3).

Front

What is the radius of the circle in the equation (x + 1)² + (y - 4)² = 25?

Back

Radius is 5 units (r = √25).

Front

How do you graph a circle given its equation?

Back

1. Identify the center (h, k). 2. Determine the radius r. 3. Plot the center and use the radius to draw the circle.

Front

What does the equation (x - 1)² + (y - 2)² = 9 represent?

Back

A circle with center (1, 2) and radius 3 units.

Front

What is the effect of changing the value of h in the equation (x - h)² + (y - k)² = r²?

Back

Changing h moves the circle left or right on the coordinate plane.

Front

What is the effect of changing the value of k in the equation (x - h)² + (y - k)² = r²?

Back

Changing k moves the circle up or down on the coordinate plane.

Front

If a circle's equation is (x + 4)² + (y - 1)² = 36, what are the coordinates of the center?

Back

Center is (-4, 1).