Conics Sections Flashcard

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 defines a circle?

Back

A circle is a conic section where all points are equidistant from a fixed center point. The standard equation is (x-h)² + (y-k)² = r².

Front

What is an ellipse?

Back

An ellipse is a conic section formed when a plane intersects a cone at an angle, resulting in a closed curve. The standard equation is (x-h)²/a² + (y-k)²/b² = 1.

Front

What is a hyperbola?

Back

A hyperbola is a conic section formed when a plane intersects both halves of a double cone. The standard equation is (x-h)²/a² - (y-k)²/b² = 1.

Front

What is a parabola?

Back

A parabola is a conic section that results from a plane intersecting a cone parallel to its slope. The standard equation is y = ax² + bx + c.

Front

What are the foci of an ellipse?

Back

The foci of an ellipse are two fixed points located along the major axis, where the sum of the distances from any point on the ellipse to the foci is constant.

Front

What are the vertices of a hyperbola?

Back

The vertices of a hyperbola are the points where the hyperbola intersects its transverse axis, representing the closest points of the two branches.

Front

How do you identify a conic section from its equation?

Back

You can identify a conic section by analyzing the equation's format. For example, if both x² and y² terms are present with the same sign, it's a circle or ellipse; if they have different signs, it's a hyperbola.

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 is the difference between an ellipse and a hyperbola?

Back

An ellipse is a closed curve with two foci, while a hyperbola consists of two separate curves (branches) with two foci.