Conic Sections

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

(x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

What is the standard equation of an ellipse?

Back

(x - h)²/a² + (y - k)²/b² = 1, where (h, k) is the center, a is the semi-major axis, and b is the semi-minor axis.

Front

What is the standard equation of a hyperbola?

Back

(x - h)²/a² - (y - k)²/b² = 1 or (y - k)²/b² - (x - h)²/a² = 1, where (h, k) is the center.

Front

What is the standard equation of a parabola that opens upwards?

Back

(x - h)² = 4p(y - k), where (h, k) is the vertex and p is the distance from the vertex to the focus.

Front

What is the focus of a parabola?

Back

The focus is a point from which distances to points on the parabola are measured.

Front

What is the directrix of a parabola?

Back

The directrix is a line used in the definition of a parabola, where each point on the parabola is equidistant from the focus and the directrix.

Front

How do you find the foci of an ellipse?

Back

The foci are located at (h ± c, k) for horizontal ellipses and (h, k ± c) for vertical ellipses, where c = √(a² - b²).

Front

What is the difference between a circle and an ellipse?

Back

A circle is a special case of an ellipse where the lengths of the semi-major and semi-minor axes are equal.

Front

What is the definition of a hyperbola?

Back

A hyperbola is a set of all points where the difference of the distances to two fixed points (foci) is constant.