Unit 7 Circles Study Guide

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 radius of a circle given its equation?

Back

The radius is the square root of the constant on the right side of the equation in standard form.

Front

What does the center of a circle represent in its equation?

Back

The center (h, k) is the point around which the circle is drawn.

Front

If a circle has a center at (3, -4) and a radius of 5, what is its equation?

Back

(x - 3)² + (y + 4)² = 25.

Front

What is the area of a circle with radius r?

Back

Area = πr².

Front

How do you calculate the area of a sector of a circle?

Back

Area of sector = (θ/360) × πr², where θ is the angle in degrees.

Front

What is the relationship between the diameter and radius of a circle?

Back

Diameter = 2 × Radius.

Front

What is the circumference of a circle with radius r?

Back

Circumference = 2πr.

Front

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

Back

Complete the square for both x and y terms.

Front

What is the significance of the coordinates in the equation of a circle?

Back

They determine the position of the circle in the coordinate plane.