Equations of 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 do the variables h and k represent in the circle equation?

Back

h and k represent the x and y coordinates of the center of the circle, respectively.

Front

How do you find the center of a circle from its equation?

Back

The center can be found from the equation (x-h)² + (y-k)² = r² by identifying h and k.

Front

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

Back

The radius is 5, since r² = 25, thus r = √25 = 5.

Front

What is the center of the circle in the equation (x+3)² + (y-1)² = 36?

Back

The center is (-3, 1).

Front

What is the radius of the circle in the equation (x-1)² + (y-3)² = 4?

Back

The radius is 2, since r² = 4, thus r = √4 = 2.

Front

How do you convert the general form of a circle's equation to standard form?

Back

Complete the square for both x and y terms to rewrite the equation in the form (x-h)² + (y-k)² = r².

Front

What is the center and radius of the circle with equation (x-2)² + (y+3)² = 9?

Back

Center is (2, -3) and radius is 3.

Front

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

Back

The equation is x² + y² = 25.

Front

What does the number on the right side of the equation (x-h)² + (y-k)² = r² represent?

Back

It represents the square of the radius (r²) of the circle.