Classifying Conic Sections (Graphs)

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 general equation of a circle?

Back

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

Front

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

Back

The standard form of the equation of an ellipse centered at (h, k) is (x - h)²/a² + (y - k)²/b² = 1, where a and b are the semi-major and semi-minor axes.

Front

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

Back

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

Front

What is the definition of a parabola?

Back

A parabola is a conic section that is formed by the intersection of a cone and a plane parallel to its side. It can be represented by the equation y = ax² + bx + c.

Front

How do you identify a circle from its equation?

Back

A circle can be identified from its equation if it is in the form (x - h)² + (y - k)² = r², where r is the radius.

Front

What is the difference between an ellipse and a circle?

Back

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

Front

What is the equation of a circle with center (0, 0) and radius 5?

Back

The equation is x² + y² = 25.

Front

What is the equation of an ellipse with center (0, 0), semi-major axis 4, and semi-minor axis 3?

Back

The equation is x²/16 + y²/9 = 1.

Front

What is the equation of a hyperbola with center (0, 0), transverse axis 6, and conjugate axis 4?

Back

The equation is x²/9 - y²/16 = 1.