Bell Ringer 12/4

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, a is the semi-major axis, and b is the semi-minor axis.

Front

How do you find the vertices of an ellipse?

Back

To find the vertices of an ellipse, identify the center (h,k) and add/subtract the length of the semi-major axis (a) from the h-coordinate for horizontal ellipses or the k-coordinate for vertical ellipses.

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 for horizontal hyperbolas and (y-k)²/a² - (x-h)²/b² = 1 for vertical hyperbolas.

Front

How do you determine the direction a hyperbola opens?

Back

A hyperbola opens horizontally if the x-term is positive and vertically if the y-term is positive in its standard form.

Front

What is the formula for the distance between the foci of a hyperbola?

Back

The distance between the foci of a hyperbola is given by 2c, where c = √(a² + b²).

Front

What is the equation of a circle given its center and radius?

Back

The equation of a circle with center (h,k) and radius r is (x-h)² + (y-k)² = r².

Front

How do you find the center of a circle from its diameter endpoints?

Back

The center of a circle can be found by averaging the x-coordinates and y-coordinates of the endpoints of the diameter: ((x1+x2)/2, (y1+y2)/2).

Front

What are the coordinates of the vertices of a hyperbola?

Back

The vertices of a hyperbola are located at (h±a, k) for horizontal hyperbolas and (h, k±a) for vertical hyperbolas.

Front

What is the relationship between the semi-major axis and the semi-minor axis in an ellipse?

Back

In an ellipse, the semi-major axis (a) is always greater than or equal to the semi-minor axis (b).

Front

How do you convert the general form of a conic section to standard form?

Back

To convert the general form of a conic section to standard form, complete the square for both x and y terms.