Classifying Conic Sections (Graphs)

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.

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

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.

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.

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.

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.

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.

The equation is x² + y² = 25.

The equation is x²/16 + y²/9 = 1.

The equation is x²/9 - y²/16 = 1.