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

Back

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

Front

If the diameter of a circle is 12, what is the radius?

Back

The radius is 6.

Front

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

Back

The diameter is twice the radius.

Front

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

Back

x² + y² = 25.

Front

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

Back

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

Front

What is the diameter of a circle represented by the equation (x-4)²+(y-3)²=25?

Back

The diameter is 10.

Front

What is the radius of a circle represented by the equation (x+1)² + (y+1)² = 9?

Back

The radius is 3.

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.

Front

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

Back

Ax² + Ay² + Bx + Cy + D = 0.