Conic Sections Review

Front

What is a parabola?

Back

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

Front

What is the standard form of a parabola that opens upwards?

Back

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

Front

What is the standard form of a parabola that opens downwards?

Back

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

Front

What is the standard form of a parabola that opens to the right?

Back

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

Front

What is the standard form of a parabola that opens to the left?

Back

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

Front

How do you determine the direction a parabola opens based on its equation?

Back

If the coefficient of the squared term is positive, it opens upwards or to the right; if negative, it opens downwards or to the left.

Front

What is the general equation of a circle?

Back

The general 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 is the center and radius of the circle given by (x + 3)² + (y - 4)² = 9?

Back

Center: (-3, 4), Radius: 3.

Front

What is the standard form of an ellipse?

Back

The standard form 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 identify 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. If a > b, the major axis is horizontal; if b > a, it is vertical.