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

The center of a circle in the equation (x - h)² + (y - k)² = r² is given by the coordinates (h, k).

Front

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

Back

The radius (r) in the equation (x - h)² + (y - k)² = r² represents the distance from the center of the circle to any point on the circle.

Front

What are the coordinates of the center of the circle given by the equation x² + y² = 16?

Back

The center is (0, 0).

Front

If a circle has a center at (2, -3) and a radius of 4, what is its equation?

Back

The equation is (x - 2)² + (y + 3)² = 16.

Front

What is the radius of a circle with the equation (x + 1)² + (y - 2)² = 25?

Back

The radius is 5 units.

Front

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

Back

Substitute the point's coordinates into the circle's equation. If the result is less than r², the point is inside; if equal, on the circle; if greater, outside.

Front

What is the equation of a circle with center (0, 0) and radius 1?

Back

The equation is x² + y² = 1.

Front

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

Back

The diameter is twice the radius (d = 2r).

Front

What is the equation of a circle with center (5, 5) and radius 3?

Back

The equation is (x - 5)² + (y - 5)² = 9.