Equations of Circles and 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 is the center of the circle in the equation (x - 2)² + (y + 3)² = 25?

Back

(2, -3)

Front

What is the radius of the circle in the equation (x + 4)² + (y - 1)² = 36?

Back

6

Front

What are the coordinates of the center of the circle given by the equation x² + y² = 49?

Back

(0, 0)

Front

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

Back

x² + y² = 25

Front

What is the general 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

What are the foci of the ellipse given by the equation (x - 1)²/16 + (y + 2)²/9 = 1?

Back

(1 ± √7, -2)

Front

What is the distance between the foci of an ellipse with a = 5 and b = 3?

Back

2√(a² - b²) = 2√(25 - 9) = 2√16 = 8

Front

What is the equation of an ellipse with center (0, 0), semi-major axis 4, and semi-minor axis 3?

Back

(x²/16) + (y²/9) = 1

Front

What is the relationship between the lengths of the axes of an ellipse?

Back

The length of the major axis is greater than the length of the minor axis.