Conic Sections

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 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 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 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, where (h, k) is the center.

Front

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

Back

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

Front

How do you identify a hyperbola from its equation?

Back

A hyperbola can be identified by the presence of a subtraction sign between the squared terms in its equation.

Front

What is the center of the circle represented by (x - 3)² + (y + 5)² = 16?

Back

The center of the circle is (3, -5).

Front

What is the radius of the circle represented by (x - 2)² + (y + 4)² = 9?

Back

The radius of the circle is 3.

Front

What is the difference between an ellipse and a circle?

Back

An ellipse is a stretched circle, defined by two foci, while a circle is a special case of an ellipse where both foci coincide at the center.

Front

What are the foci of a hyperbola?

Back

The foci of a hyperbola are two fixed points located along the transverse axis, used to define the hyperbola.