Ellipses and Circles Practice

Front

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

Back

The standard form is \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) where \( a > b \).

Front

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

Back

The standard form is \( \frac{y^2}{a^2} + \frac{x^2}{b^2} = 1 \) where \( a > b \).

Front

What are the coordinates of the foci of an ellipse?

Back

The foci are located at (\( \pm c, 0 \)) for horizontal ellipses and (0, \( \pm c \)) for vertical ellipses, where \( c = \sqrt{a^2 - b^2} \).

Front

What is the definition of the vertices of an ellipse?

Back

The vertices are the endpoints of the major axis of the ellipse.

Front

How do you find the length of the major axis of an ellipse?

Back

The length of the major axis is \( 2a \), where \( a \) is the semi-major axis.

Front

How do you find the length of the minor axis of an ellipse?

Back

The length of the minor axis is \( 2b \), where \( b \) is the semi-minor axis.

Front

What is the relationship between the semi-major axis, semi-minor axis, and the distance to the foci in an ellipse?

Back

The relationship is given by \( c^2 = a^2 - b^2 \).

Front

What are the coordinates of the co-vertices of an ellipse?

Back

The co-vertices are located at (0, \( \pm b \)) for horizontal ellipses and (\( \pm b, 0 \)) for vertical ellipses.

Front

What is the definition of eccentricity in relation to an ellipse?

Back

Eccentricity (e) is defined as \( e = \frac{c}{a} \), where \( c \) is the distance from the center to a focus and \( a \) is the distance from the center to a vertex.

Front

What is the formula to find the area of an ellipse?

Back

The area of an ellipse is given by the formula \( A = \pi a b \).