ID the Conic and Equations from Graphs

Front

What is a hyperbola?

Back

A hyperbola is a type of conic section that appears as two separate curves, defined as the set of all points where the difference of the distances to two fixed points (foci) is constant.

Front

What is the standard equation of a hyperbola centered at the origin?

Back

The standard equation is (x^2/a^2) - (y^2/b^2) = 1 for a horizontal hyperbola and (y^2/a^2) - (x^2/b^2) = 1 for a vertical hyperbola.

Front

Identify the conic: (y - 1)^2 / 9 - (x - 0)^2 / 25 = 1

Back

This is a hyperbola.

Front

What is a parabola?

Back

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

Front

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

Back

The standard equation 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

Identify the conic: (x - 3) = (y - 5)^2

Back

This is a parabola.

Front

What is an ellipse?

Back

An ellipse is a conic section that appears as an elongated circle, defined as the set of all points where the sum of the distances to two fixed points (foci) is constant.

Front

What is the standard equation of an ellipse centered at the origin?

Back

The standard equation is (x^2/a^2) + (y^2/b^2) = 1, where a and b are the semi-major and semi-minor axes, respectively.

Front

Identify the conic: (x - 0)^2 / 25 - (y - 1)^2 / 9 = 1

Back

This is a hyperbola.

Front

What is the difference between a circle and an ellipse?

Back

A circle is a special case of an ellipse where the two foci coincide at the center, and the distances to the foci are equal.