Alg. 2 Review: Circle Equations

Front

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

Back

The standard 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

How do you find the radius of a circle given its center and a point on the circle?

Back

Use the distance formula: r = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) is the center and (x2, y2) is the point on the circle.

Front

Calculate the radius of a circle with center (2, 2) and a point on the circle at (6, 6).

Back

r = √((6 - 2)² + (6 - 2)²) = √(16 + 16) = √32 = 4√2.

Front

What does it mean for a function to be odd?

Back

A function f(x) is odd if f(-x) = -f(x) for all x in the domain.

Front

Given g(2.5) = 4, what is g(-2.5) if g(x) is an odd function?

Back

g(-2.5) = -4.

Front

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

Back

Complete the square for both x and y terms in the equation Ax² + Ay² + Bx + Cy + D = 0.

Front

Convert the equation x² + y² + 6x - 12y + 20 = 0 to standard form.

Back

(x + 3)² + (y - 6)² = 25.

Front

What is the significance of the center and radius in a circle's equation?

Back

The center (h, k) determines the location of the circle, and the radius r determines its size.

Front

What is the slope of a line through two points (x1, y1) and (x2, y2)?

Back

The slope m is given by m = (y2 - y1) / (x2 - x1).

Front

Find the slope of the line through (6, 1) and (8, 7).

Back

m = (7 - 1) / (8 - 6) = 6 / 2 = 3.