Conic Sections (Post Test)

Front

What are conic sections?

Back

Conic sections are the curves obtained by intersecting a plane with a double-napped cone. The main types 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 the definition of a parabola?

Back

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

Front

What is the major axis of an ellipse?

Back

The major axis of an ellipse is the longest diameter that passes through the center and both foci of the ellipse.

Front

What is the minor axis of an ellipse?

Back

The minor axis of an ellipse is the shortest diameter that is perpendicular to the major axis at the center.

Front

How do you find the center of a hyperbola?

Back

The center of a hyperbola can be found at the midpoint of the line segment that connects its two foci.

Front

What is the equation of a hyperbola?

Back

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

Front

What are the foci of an ellipse?

Back

The foci of an ellipse are two fixed points located along the major axis, such that the sum of the distances from any point on the ellipse to the foci is constant.

Front

What is the relationship between the eccentricity and the type of conic section?

Back

Eccentricity (e) determines the type of conic section: e = 0 for a circle, 0 < e < 1 for an ellipse, e = 1 for a parabola, and e > 1 for a hyperbola.

Front

What is the distance formula used to find the distance between two points?

Back

The distance d between two points (x1, y1) and (x2, y2) is given by d = √((x2 - x1)² + (y2 - y1)²).