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 radius from the equation of a circle?

Back

The radius is the square root of the number on the right side of the equation in standard form.

Front

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

Back

Center is (2, -3).

Front

What is the radius of the circle represented by the equation (x+1)² + (y-4)² = 49?

Back

Radius is 7 units.

Front

What is the diameter of a circle if the radius is 5 units?

Back

Diameter is 10 units.

Front

What is the equation of a circle with center at (0,0) and radius 4?

Back

The equation is x² + y² = 16.

Front

If a circle has the equation (x+5)² + (y-2)² = 36, what is the radius?

Back

Radius is 6 units.

Front

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

Back

The general form is x² + y² + Dx + Ey + F = 0.

Front

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

Back

Complete the square for x and y terms.