Conic Sections Review

Front

What is a conic section?

Back

A conic section is a curve obtained by intersecting a cone with a plane. The four types of conic sections are circles, ellipses, parabolas, and hyperbolas.

Front

What is the standard form of a hyperbola with a vertical transverse axis?

Back

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

Front

What is the standard form of a hyperbola with a horizontal transverse axis?

Back

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

Front

What are the asymptotes of a hyperbola?

Back

The asymptotes are the lines that the hyperbola approaches but never touches. For a hyperbola centered at (h, k), the equations are y = k ± (b/a)(x - h) for a horizontal transverse axis.

Front

How do you find the foci of a hyperbola?

Back

The foci are located at a distance of c from the center along the transverse axis, where c = √(a² + b²).

Front

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

Back

In a hyperbola, c² = a² + b², where a is the distance from the center to the vertices and b is the distance from the center to the co-vertices.

Front

What is the definition of a vertex in a hyperbola?

Back

A vertex is a point where the hyperbola intersects its transverse axis.

Front

What is the definition of a co-vertex in a hyperbola?

Back

A co-vertex is a point where the hyperbola intersects its conjugate axis.

Front

How do you determine if a hyperbola is vertical or horizontal?

Back

If the equation is in the form (y - k)²/a² - (x - h)²/b² = 1, it is vertical. If it is in the form (x - h)²/a² - (y - k)²/b² = 1, it is horizontal.

Front

What is the equation of a hyperbola centered at (h, k) with a vertical transverse axis?

Back

The equation is (y - k)²/a² - (x - h)²/b² = 1.