Conic sections Review

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 equation of a circle?

Back

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

Front

What distinguishes an ellipse from a circle?

Back

An ellipse is a stretched circle, defined by two foci, while a circle has a constant radius from its center.

Front

What is the standard equation of an ellipse?

Back

The standard 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 a hyperbola?

Back

A hyperbola is a type of conic section formed by the intersection of a plane and a double cone, characterized by two separate curves.

Front

What is the standard equation of a hyperbola?

Back

The standard equation of a hyperbola centered at (h, k) is ((x - h)²/a²) - ((y - k)²/b²) = 1 for horizontal hyperbolas, and vice versa for vertical hyperbolas.

Front

What is a parabola?

Back

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

Front

What is the standard equation of a parabola?

Back

The standard equation of a parabola that opens upwards is (x - h)² = 4p(y - k), where (h, k) is the vertex and p is the distance from the vertex to the focus.

Front

How can you identify a circle from its equation?

Back

A circle's equation will have the form (x - h)² + (y - k)² = r², where r is the radius.

Front

What is the difference between the equations of a circle and an ellipse?

Back

A circle has equal coefficients for x² and y², while an ellipse has different coefficients.