Circles & Ellipses

Front

What is the standard equation of a circle with center (h, k) and radius r?

Back

(x - h)² + (y - k)² = r²

Front

What are the coordinates of the center and radius of the circle given by the equation (x - 3)² + (y + 2)² = 16?

Back

Center: (3, -2), Radius: 4 units

Front

How do you find the radius of a circle if you know the diameter?

Back

Radius = Diameter / 2

Front

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

Back

Area = π * r², where r is the radius.

Front

What is the equation of a circle with center at the origin and radius 5?

Back

x² + y² = 25

Front

What are the coordinates of the center and radius of the circle given by the equation (x + 1)² + (y - 4)² = 9?

Back

Center: (-1, 4), Radius: 3 units

Front

What is the standard form of the equation of an ellipse?

Back

(x - h)²/a² + (y - k)²/b² = 1, where (h, k) is the center, a is the semi-major axis, and b is the semi-minor axis.

Front

How do you determine the foci of an ellipse?

Back

Foci are located at (h ± c, k) for horizontal ellipses and (h, k ± c) for vertical ellipses, where c = √(a² - b²).

Front

What is the relationship between the axes of an ellipse?

Back

The length of the major axis is 2a and the length of the minor axis is 2b.

Front

What is the equation of a circle with center (0, 0) and radius 10?

Back

x² + y² = 100