Ellipses

Front

What are the coordinates of the CO-VERTICES of an ellipse centered at (0,0) with a vertical major axis and lengths a=5, b=3?

Back

(0, 5) and (0, -5)

Front

What is the standard form equation of an ellipse with a horizontal major axis?

Back

(x-h)²/a² + (y-k)²/b² = 1, where (h,k) is the center.

Front

What is the standard form equation of an ellipse with a vertical major axis?

Back

(x-h)²/b² + (y-k)²/a² = 1, where (h,k) is the center.

Front

What do the variables a, b, and c represent in the context of an ellipse?

Back

a = semi-major axis, b = semi-minor axis, c = distance from center to foci.

Front

If an ellipse has a center at (2,3) and a semi-major axis of length 4, what are the coordinates of the vertices?

Back

(2, 7) and (2, -1)

Front

What is the relationship between a, b, and c in an ellipse?

Back

c² = a² - b².

Front

What are the coordinates of the foci of an ellipse centered at (0,0) with a=5 and b=3?

Back

(±4, 0)

Front

How can you determine if an ellipse is wide or tall based on the values of a and b?

Back

If a > b, the ellipse is wide; if a < b, the ellipse is tall.

Front

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

Back

2c = 2√(a² - b²) = 2√(25 - 9) = 2√16 = 8.

Front

What are the coordinates of the vertices of an ellipse with a center at (1,2) and a semi-minor axis of length 3?

Back

(1, 5) and (1, -1)