Conics Review

Front

What is the standard form of the equation of a circle?

Back

(x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

How do you find the center of a circle from its equation?

Back

The center (h, k) can be found from the equation (x - h)² + (y - k)² = r².

Front

What is the radius of a circle given the equation (x - 4)² + (y - 3)² = 25?

Back

The radius is 5 units, since r² = 25.

Front

What are the characteristics of an ellipse?

Back

An ellipse has two foci, a major axis, and a minor axis.

Front

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

Back

(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 a hyperbola from its equation?

Back

A hyperbola has the form (x - h)²/a² - (y - k)²/b² = 1 or (y - k)²/b² - (x - h)²/a² = 1.

Front

What is the center of the ellipse given by the equation (x - 1)²/4 + (y - 0)²/9 = 1?

Back

The center is (1, 0).

Front

What is the definition of a conic section?

Back

A conic section is a curve obtained by intersecting a cone with a plane.

Front

What are the four types of conic sections?

Back

Circle, Ellipse, Parabola, Hyperbola.

Front

How do you find the foci of an ellipse?

Back

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