Precalculus 1st Semester Review

Front

What is the general form of a circle's equation?

Back

The general 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 standard form of a parabola that opens upwards?

Back

The standard form of a parabola that opens upwards is y = a(x - h)² + k, where (h, k) is the vertex.

Front

What is the equation of an ellipse in standard form?

Back

Front

What is the definition of a hyperbola?

Back

A hyperbola is a set of all points (x, y) such that the absolute difference of the distances from two fixed points (foci) is constant.

Front

What is the standard form of a hyperbola?

Back

Front

How do you determine if a conic section is a circle, ellipse, or hyperbola from its equation?

Back

You can determine the type of conic section by examining the coefficients of x² and y². If they are equal and have the same sign, it's a circle; if they are equal but have different signs, it's a hyperbola; if they are different but both positive, it's an ellipse.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the point where the parabola changes direction, represented as (h, k) in the standard form y = a(x - h)² + k.

Front

What is the focus of a parabola?

Back

The focus of a parabola is a fixed point located along the axis of symmetry, which is used to define the parabola's shape.

Front

What is the directrix of a parabola?

Back

The directrix of a parabola is a line perpendicular to the axis of symmetry, and it is used in conjunction with the focus to define the parabola.

Front

What is the difference between a vertical and horizontal hyperbola?

Back

A vertical hyperbola opens upwards and downwards, while a horizontal hyperbola opens left and right. This is determined by the placement of the squared terms in the standard form.