Conics - Ellipses

Front

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

Back

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

Front

What do the variables 'a' and 'b' represent in the standard equation of an ellipse?

Back

'a' represents the semi-major axis length, and 'b' represents the semi-minor axis length.

Front

How do you find 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

If the foci of an ellipse are 40 feet apart, what is the distance from the center to each focus?

Back

The distance from the center to each focus is 20 feet.

Front

What is the relationship between the lengths of the axes and the foci in an ellipse?

Back

The distance between the foci is less than the length of the major axis.

Front

What is the length of the major axis if the semi-major axis is 'a'?

Back

The length of the major axis is \( 2a \).

Front

What is the length of the minor axis if the semi-minor axis is 'b'?

Back

The length of the minor axis is \( 2b \).

Front

In an ellipse, if the major axis is 50 feet long, what is the length of the semi-major axis?

Back

The length of the semi-major axis is 25 feet.

Front

Given the foci (-3, 4) and (-3, 0), what is the center of the ellipse?

Back

The center of the ellipse is at (-3, 2).