Conics Review

Front

What are the foci of a hyperbola?

Back

The foci of a hyperbola are the two fixed points located along the transverse axis, which help define the shape of the hyperbola.

Front

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

Back

The standard form of a hyperbola centered at (h, k) is: (x-h)²/a² - (y-k)²/b² = 1 (horizontal) or (y-k)²/a² - (x-h)²/b² = 1 (vertical).

Front

How do you find the vertices of a hyperbola?

Back

The vertices of a hyperbola are located a units away from the center along the transverse axis. For the equation (x-h)²/a² - (y-k)²/b² = 1, the vertices are (h±a, k).

Front

What is the center of a circle given by the equation (x - h)² + (y - k)² = r²?

Back

The center of the circle is the point (h, k).

Front

What is the radius of a circle given by the equation (x - h)² + (y - k)² = r²?

Back

The radius of the circle is the square root of r².

Front

What are the asymptotes of a hyperbola?

Back

The asymptotes of a hyperbola are the lines that the hyperbola approaches as it extends to infinity. They can be found using the formula y = k ± (b/a)(x-h) for a horizontal hyperbola.

Front

How do you determine the equation of the asymptotes for a hyperbola?

Back

For a hyperbola in standard form, the asymptotes can be found using the equations y = k ± (b/a)(x-h) for horizontal hyperbolas and y = k ± (a/b)(x-h) for vertical hyperbolas.

Front

What is the relationship between the foci, vertices, and center of a hyperbola?

Back

The distance from the center to each focus is c, and the distance from the center to each vertex is a. The relationship is given by c² = a² + b².

Front

What is the equation of a circle with center (h, k) and radius r?

Back

The equation of a circle is (x - h)² + (y - k)² = r².

Front

How do you graph a hyperbola?

Back

To graph a hyperbola, identify the center, vertices, and foci, draw the asymptotes, and sketch the branches of the hyperbola approaching the asymptotes.