Conic Sections Review 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 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 eccentricity in relation to conic sections?

Back

Eccentricity is a measure of how much a conic section deviates from being circular. It is defined as the ratio of the distance from a point on the conic to a focus and the distance from that point to the nearest directrix.

Front

What is the equation of an ellipse in standard form?

Back

The standard form of an ellipse's equation is (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

How do you find the center of a circle from its equation?

Back

To find the center of a circle from its equation in the form x² + y² + Dx + Ey + F = 0, rearrange it to (x - h)² + (y - k)² = r², where h = -D/2 and k = -E/2.

Front

What are the characteristics of an ellipse?

Back

An ellipse has two foci, a major axis, a minor axis, and its eccentricity is less than 1. The distance between the foci is related to the lengths of the axes.

Front

What is the relationship between the foci and vertices of an ellipse?

Back

The distance from the center to a focus (c) and the distance from the center to a vertex (a) are related by the equation c² = a² - b², where b is the semi-minor axis.

Front

What is the equation of a parabola in standard form?

Back

The standard form of a parabola's equation is y = a(x - h)² + k or x = a(y - k)² + h, where (h, k) is the vertex.

Front

How do you convert a general quadratic equation to standard form?

Back

To convert a general quadratic equation Ax² + Bxy + Cy² + Dx + Ey + F = 0 to standard form, complete the square for the x and y terms.

Front

What is the definition of a hyperbola?

Back

A hyperbola is a type of conic section formed by the intersection of a plane and both halves of a double cone. It consists of two separate curves called branches.