Conics Flashcard

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

Identify the general form of a conic section.

Back

Ax² + Bxy + Cy² + Dx + Ey + F = 0, where A, B, C, D, E, and F are constants.

Front

What is the definition of an ellipse?

Back

A set of points where the sum of the distances from two fixed points (foci) is constant.

Front

What is the center of an ellipse given by the equation (x - h)²/a² + (y - k)²/b² = 1?

Back

The center is (h, k).

Front

How do you determine if a conic section is a hyperbola?

Back

If the equation can be written in 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 definition of a parabola?

Back

A set of points equidistant from a fixed point (focus) and a fixed line (directrix).

Front

What is the formula for the distance between the foci of a hyperbola?

Back

2c, where c = √(a² + b²).

Front

Identify the conic section represented by the equation 4x² - 5y² + 2x - 8y + 10 = 0.

Back

Hyperbola.

Front

What is the relationship between a, b, and c in an ellipse?

Back

c² = a² - b², where a is the semi-major axis and b is the semi-minor axis.

Front

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

Back

y = a(x - h)² + k, where (h, k) is the vertex.