Conic Sections (Choice Board)

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 circle's equation?

Back

The standard form of a circle's equation is (x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.

Front

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

Back

The center of a circle in the equation (x-h)² + (y-k)² = r² is given by the point (h, k).

Front

What is the formula for the radius of a circle?

Back

The radius of a circle is the square root of the value on the right side of the equation in standard form: r = √(value).

Front

What are the key characteristics of an ellipse?

Back

An ellipse has two foci, a major axis, a minor axis, and the sum of the distances from any point on the ellipse to the two foci is constant.

Front

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

Back

The standard form of an ellipse's equation 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 identify the vertices of an ellipse?

Back

The vertices of an ellipse are located at (h±a, k) and (h, k±b) depending on the orientation of the ellipse.

Front

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

Back

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

Front

What are the key characteristics of a hyperbola?

Back

A hyperbola has two branches, two foci, and the difference of the distances from any point on the hyperbola to the two foci is constant.

Front

How do you find the center of a hyperbola?

Back

The center of a hyperbola in the equation (x-h)²/a² - (y-k)²/b² = 1 is given by the point (h, k).