Conics

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

What defines a parabola?

Back

A parabola is defined as the set of all points that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

Front

What is the general equation of a hyperbola?

Back

The general equation of a hyperbola is (x - h)²/a² - (y - k)²/b² = 1 or (y - k)²/a² - (x - h)²/b² = 1, where (h, k) is the center.

Front

How do you identify a vertical hyperbola?

Back

A vertical hyperbola has the form (y - k)²/a² - (x - h)²/b² = 1, where the y-term is positive.

Front

What is the center of a circle given by (x - 4)² + (y - 3)² = 25?

Back

The center of the circle is (4, 3).

Front

What is the radius of a circle given by (x + 2)² + (y - 5)² = 5?

Back

The radius of the circle is √5.

Front

What is the difference between an ellipse and a circle?

Back

An ellipse is a stretched circle, defined by two foci, while a circle is a special case of an ellipse where both foci coincide at the center.

Front

What is the equation of a horizontal hyperbola?

Back

The equation of a horizontal hyperbola is (x - h)²/a² - (y - k)²/b² = 1, where (h, k) is the center.

Front

How do you find the radius from the equation of a circle?

Back

The radius can be found by taking the square root of the constant on the right side of the equation in standard form: (x - h)² + (y - k)² = r².