Circles and Ellipses

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 are the coordinates of the center and radius of the circle with equation (x - 4)² + (y - 3)² = 25?

Back

Center (4,3), Radius = 5 units.

Front

What is the equation of a circle with center (3, 4) and radius 2?

Back

(x-3)² + (y-4)² = 4.

Front

What is the equation of the circle with center (-1, -1) and radius 3?

Back

(x+1)² + (y+1)² = 9.

Front

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

Back

x² + y² + Dx + Ey + F = 0, where D, E, and F are constants.

Front

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

Back

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

Front

What is the center of the circle given by the equation (x+2)² + (y-5)² = 16?

Back

Center (-2, 5).

Front

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

Back

Diameter = 2 * Radius.

Front

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

Back

x² + y² = 16.

Front

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

Back

Complete the square for x and y terms.