Circle Equations and Graphs

Front

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

Back

The standard form of the equation of a circle 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 diameter?

Back

The radius is half the length of the diameter. If the diameter is d, then the radius r = d/2.

Front

What is the center of a circle in the equation (x - h)² + (y - k)² = r²?

Back

The center of the circle is the point (h, k).

Front

What does it mean for x to vary inversely as v?

Back

It means that as x increases, v decreases, and vice versa, such that x * v = k, where k is a constant.

Front

How do you convert the diameter of a circle to its radius?

Back

Divide the diameter by 2 to get the radius.

Front

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

Back

The area A of a circle is given by the formula A = πr², where r is the radius.

Front

What is the equation of a circle with center (0, 0) and radius 5?

Back

The equation is x² + y² = 25.

Front

How do you determine the equation of a circle given its center and radius?

Back

Use the formula (x - h)² + (y - k)² = r², substituting the center (h, k) and radius r.

Front

What is the significance of the number 9 in the equation (x - 7)² + y² = 9?

Back

The number 9 represents the square of the radius, so the radius is 3.

Front

What type of variation is represented by the equation y = kx?

Back

This represents direct variation, where y varies directly with x.