Conics

Front

What is a conic section?

Back

A conic section is a curve obtained by intersecting a cone with a plane. The four types of conic sections 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 defines a parabola?

Back

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

Front

What is the general equation of a parabola that opens upwards?

Back

The general equation of a parabola that opens upwards is y = ax² + bx + c, where a > 0.

Front

How do you find the vertex of a parabola given its equation in standard form?

Back

For a parabola in the form y = a(x - h)² + k, the vertex is at the point (h, k).

Front

What is the equation of a circle with center (h, k) and radius r?

Back

The equation of a circle is (x - h)² + (y - k)² = r².

Front

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

Back

The standard form of an ellipse's equation 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

What is the difference between a major and minor axis in an ellipse?

Back

The major axis is the longest diameter of the ellipse, while the minor axis is the shortest diameter.

Front

What is the standard form of a hyperbola's equation?

Back

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

Front

How do you find the foci of an ellipse?

Back

The foci of an ellipse are located at (h ± c, k) for a horizontal ellipse and (h, k ± c) for a vertical ellipse, where c = √(a² - b²).