🟣Conic Sections 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 given its equation in standard form?

Back

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

Front

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

Back

The radius is 4 units, since r² = 16.

Front

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

Back

x² + y² + Dx + Ey + F = 0, where D, E, and F are constants.

Front

How do you convert the general form of a circle's equation to standard form?

Back

Complete the square for x and y terms.

Front

What is the distance formula used to find the distance between two points (x1, y1) and (x2, y2)?

Back

d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the definition of an ellipse?

Back

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

Front

What is the standard form of the equation of an ellipse centered at (h, k)?

Back

(x - h)²/a² + (y - k)²/b² = 1, where a and b are the semi-major and semi-minor axes.

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 c² = a² - b².

Front

What is the definition of a hyperbola?

Back

A hyperbola is the set of all points where the absolute difference of the distances from two fixed points (foci) is constant.