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 radius of a circle from its equation?

Back

To find the radius of a circle from its equation in standard form (x - h)² + (y - k)² = r², take the square root of r².

Front

What is the center of a circle in the equation (x - 3)² + (y + 2)² = 16?

Back

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

Front

If the radius of a circle is 5, what is the value of r² in the equation?

Back

If the radius is 5, then r² = 25.

Front

What does the equation x² + y² = 25 represent?

Back

The equation x² + y² = 25 represents a circle centered at the origin (0, 0) with a radius of 5.

Front

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

Back

To determine if a point (x₀, y₀) lies inside, on, or outside a circle with center (h, k) and radius r, calculate the distance from the point to the center: d = √((x₀ - h)² + (y₀ - k)²). If d < r, the point is inside; if d = r, it is on the circle; if d > r, it is outside.

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 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 radius of the circle given by the equation (x - 1)² + (y + 3)² = 36?

Back

The radius is 6, since r² = 36.

Front

What is the center of the circle represented by the equation (x + 5)² + (y - 2)² = 9?

Back

The center of the circle is (-5, 2).