Graphing Circles and Writing Equations

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 is the radius of a circle given the equation (x - 2)² + (y + 3)² = 16?

Back

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

Front

How can you determine if a point lies on a circle?

Back

To determine if a point (x, y) lies on a circle, substitute the coordinates into the circle's equation and check if the equation holds true.

Front

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

Back

The diameter of a circle is twice the radius, or d = 2r.

Front

What are the coordinates of the center of the circle given by the equation (x + 5)² + (y - 1)² = 25?

Back

The center of the circle is (-5, 1).

Front

How do 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 x and y.

Front

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

Back

The distance formula is used to find the distance between the center of the circle and a point to determine if the point lies inside, on, or outside the circle.

Front

What does the term 'radius' refer to in the context of a circle?

Back

The radius is the distance from the center of the circle to any point on its circumference.

Front

If a circle has a center at (0,0) and a radius of 3, what is its equation?

Back

The equation of the circle is x² + y² = 9.