Equations of Circles

Front

What is the standard equation of a circle?

Back

(x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.

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 defined.

Front

In the equation (x-4)² + (y-3)² = 25, what is the radius of the circle?

Back

The radius is 5, since 25 = 5².

Front

How do you find the center of a circle from its equation?

Back

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

Front

What is the diameter of a circle?

Back

The diameter is twice the radius.

Front

If the diameter of a circle is 12, what is the radius?

Back

The radius is 6.

Front

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

Back

The radius is the distance from the center to any point on the circle, represented as r in the equation.

Front

What type of conic section is represented by the equation (x-2)² + (y+3)² = 16?

Back

This equation represents a circle.

Front

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

Back

Complete the square for both x and y terms.

Front

What is the significance of the number on the right side of the circle's equation?

Back

It represents the square of the radius (r²).