Final exam for precalculus

Front

What are the vertices of an ellipse?

Back

The vertices of an ellipse are the points where the ellipse intersects its major axis. For the ellipse centered at (h, k) with semi-major axis a and semi-minor axis b, the vertices are located at (h ± a, k).

Front

What is the standard form of the equation of an ellipse?

Back

The standard form of the equation of an ellipse centered at (h, k) is: (x-h)²/a² + (y-k)²/b² = 1, where a is the semi-major axis and b is the semi-minor axis.

Front

Identify the conic section represented by the equation (x-1)²/16 - (y+2)²/4 = 1.

Back

This equation represents a hyperbola.

Front

What is the component form of a vector given two points A(x1, y1) and B(x2, y2)?

Back

The component form of the vector AB is given by ⟨x2 - x1, y2 - y1⟩.

Front

How do you find the common ratio in a geometric sequence?

Back

The common ratio r in a geometric sequence can be found by dividing any term by the previous term: r = a_n / a_(n-1).

Front

What is the equation of a circle in standard form?

Back

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

Front

What is the difference between a parabola and an ellipse?

Back

A parabola is a conic section that opens either upward or downward (or left/right) and has a single focus, while an ellipse is a closed curve with two foci.

Front

What is the formula for the area of an ellipse?

Back

The area A of an ellipse is given by the formula: A = πab, where a is the semi-major axis and b is the semi-minor axis.

Front

How do you determine the foci of an ellipse?

Back

The foci of an ellipse can be found using the formula: c = √(a² - b²), where c is the distance from the center to each focus.

Front

What is the relationship between the major and minor axes of an ellipse?

Back

The major axis is the longest diameter of the ellipse, while the minor axis is the shortest diameter, and they are perpendicular to each other.