Conics Review

Front

What are the vertices of an ellipse?

Back

The vertices of an ellipse are the points where the ellipse intersects its major axis. For example, in the ellipse centered at (3, 1) with a vertical major axis, the vertices are (3, -5) and (3, 7).

Front

What is the equation to find c on a hyperbola?

Back

The equation to find c on a hyperbola is c² = a² + b².

Front

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

Back

The standard form of the equation of an ellipse is (x-h)²/a² + (y-k)²/b² = 1, where (h, k) is the center.

Front

What is the standard form of the equation of a hyperbola?

Back

The standard form of the equation of a hyperbola is (x-h)²/a² - (y-k)²/b² = 1 or (y-k)²/a² - (x-h)²/b² = 1.

Front

What are the foci of an ellipse?

Back

The foci of an ellipse are two fixed points located along the major axis, used to define the ellipse. They are found using the formula c = √(a² - b²).

Front

What is the difference between an ellipse and a hyperbola?

Back

An ellipse is a closed curve, while a hyperbola consists of two separate curves. The equations for ellipses involve addition, while hyperbolas involve subtraction.

Front

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

Back

In a hyperbola, the relationship is given by c² = a² + b², where c is the distance from the center to the foci, a is the distance from the center to the vertices, and b is related to the distance to the asymptotes.

Front

What are the asymptotes of a hyperbola?

Back

The asymptotes of a hyperbola are lines that the hyperbola approaches but never touches. They can be found using the equations y = k ± (b/a)(x-h) for a horizontal hyperbola.

Front

How do you find the center of a conic section?

Back

The center of a conic section can be found by identifying the midpoint of the line segment connecting the foci for ellipses and hyperbolas.

Front

What is the major axis of an ellipse?

Back

The major axis of an ellipse is the longest diameter that passes through both foci and the center.