Circles in Standard Form

Front

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

Back

The standard form of a circle's equation 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 in standard form?

Back

The radius of a circle in standard form (x - h)² + (y - k)² = r² is the square root of r².

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 center of the circle given by the equation (x - 3)² + (y + 2)² = 16?

Back

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

Front

What is the radius of the circle given by the equation (x + 1)² + (y - 4)² = 25?

Back

The radius of the circle is 5.

Front

Given the endpoints of a diameter (2, 3) and (8, 7), how do you find the center of the circle?

Back

The center is the midpoint of the diameter: ((2 + 8)/2, (3 + 7)/2) = (5, 5).

Front

What is the equation of a circle with center (0, 0) and radius 4?

Back

The equation is x² + y² = 16.

Front

How do you determine if a point lies inside, on, or outside a circle?

Back

Calculate the distance from the point to the center. If d < r, the point is inside; if d = r, it's on the circle; if d > r, it's outside.

Front

What is the equation of a circle with center (-3, 2) and radius 3?

Back

The equation is (x + 3)² + (y - 2)² = 9.