Conic Sections Review 2

Front

What are the major vertices of an ellipse?

Back

The major vertices of an ellipse are the points where the ellipse intersects its major axis. For example, for the ellipse with the equation (x - 1)²/25 + (y - 0)²/16 = 1, the major vertices are (1, 5) and (1, -5).

Front

What is the center of the circle given by the equation (x - 5)² + (y + 1)² = 25?

Back

The center of the circle is the point (h, k) in the standard form (x - h)² + (y - k)² = r². For the given equation, the center is (5, -1).

Front

Write the equation of a circle with a radius of 3 and center at (-4, 6).

Back

The equation of the circle is (x + 4)² + (y - 6)² = 9.

Front

What is the center of the ellipse given by the equation (x - 1)²/4 + (y - 0)²/9 = 1?

Back

The center of the ellipse is the point (h, k) in the standard form (x - h)²/a² + (y - k)²/b² = 1. For the given equation, the center is (1, 0).

Front

What is the vertex of the parabola given by the equation y = (x + 3)² - 1?

Back

The vertex of the parabola is the point (h, k) in the standard form y = a(x - h)² + k. For the given equation, the vertex is (-3, -1).

Front

Define a parabola.

Back

A parabola is a U-shaped curve that is defined as the set of all points that are equidistant from a fixed point called the focus and a fixed line called the directrix.

Front

What is the standard form of the equation of a circle?

Back

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

Front

What are the foci of an ellipse?

Back

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

Front

What is the equation of an ellipse in standard form?

Back

The standard form of the equation of an ellipse 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 distance between the foci of an ellipse?

Back

The distance between the foci of an ellipse is given by 2c, where c = √(a² - b²), and a and b are the lengths of the semi-major and semi-minor axes, respectively.