Equation Check: 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.

Tags

CCSS.7.G.A.3

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.

Tags

CCSS.HSG.GPE.A.1

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.

Tags

CCSS.HSG.GPE.A.1

Front

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

Back

The standard form of a parabola's equation that opens upwards is (x - h)² = 4p(y - k), where (h, k) is the vertex and p is the distance from the vertex to the focus.

Front

What is the focus of a parabola?

Back

The focus of a parabola is a fixed point located along the axis of symmetry, where all points on the parabola are equidistant from the focus and the directrix.

Front

What is the directrix of a parabola?

Back

The directrix of a parabola is a line perpendicular to the axis of symmetry, which is used to define the parabola as the set of points equidistant from the focus and the directrix.

Front

What is the center of a circle given by the equation (x - 3)² + (y + 2)² = 16?

Back

The center of the circle is (3, -2).

Tags

CCSS.HSG.GPE.A.1

Front

How do you find the value of p in the equation (y - k)² = 4p(x - h)?

Back

To find the value of p, identify the distance from the vertex (h, k) to the focus. This distance is represented by p.

Front

What is the equation of a hyperbola in standard form?

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, where (h, k) is the center.

Front

What is the relationship between the foci and vertices of an ellipse?

Back

The distance from the center to each focus (c) and the distance from the center to each vertex (a) are related by the equation c² = a² - b², where b is the semi-minor axis.

Tags

CCSS.HSG.GPE.A.1