Equation of a Circle

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 center of a circle from its equation?

Back

To find the center of a circle from its equation in standard form (x-h)² + (y-k)² = r², identify the values of h and k.

Front

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

Back

The radius of a circle represents the distance from the center to any point on the circle, and it is the square root of the value on the right side of the equation in standard form.

Front

In the equation (x-3)² + (y-2)² = 16, what is the radius of the circle?

Back

The radius is 4, since r² = 16, and r = √16 = 4.

Front

What is the center of the circle represented by the equation (x+1)² + (y+1)² = 9?

Back

The center of the circle is (-1, -1).

Front

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

Back

To convert from general form Ax² + Ay² + Bx + Cy + D = 0 to standard form, complete the square for the x and y terms.

Front

What is the significance of the equation x² + y² = r²?

Back

This equation represents a circle centered at the origin (0, 0) with radius r.

Front

If a circle has a center at (0, 0) and a radius of 5, what is its equation?

Back

The equation of the circle is x² + y² = 25.

Front

What is the distance formula used for in relation to circles?

Back

The distance formula can be used to determine if a point lies inside, on, or outside a circle by comparing the distance from the point to the center with the radius.

Front

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

Back

The center of the circle is (-2, 3).