Center and Radius of Circle

Front

What is the definition of the center of a circle?

Back

The center of a circle is the point that is equidistant from all points on the circle.

Front

What is the formula for the radius of a circle?

Back

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

Front

How do you find the equation of a circle given its center and radius?

Back

The equation of a circle with center (h, k) and radius r is given by (x - h)² + (y - k)² = r².

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

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

Back

The distance formula is used to calculate the distance between two points in a coordinate plane, which can help determine if a point lies inside, on, or outside a circle.

Front

What does the term 'diameter' refer to in a circle?

Back

The diameter of a circle is the distance across the circle through the center, equal to twice the radius.

Front

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

Back

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

Front

What is the significance of the origin (0,0) in a coordinate plane?

Back

The origin is the point where the x-axis and y-axis intersect, and it serves as the reference point for all other points in the coordinate plane.

Front

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

Back

To determine if a point (x, y) lies on a circle with center (h, k) and radius r, substitute the point into the circle's equation (x - h)² + (y - k)² = r². If the equation holds true, the point lies on the circle.

Front

What is the formula for calculating the circumference of a circle?

Back

The circumference of a circle is calculated using the formula C = 2πr, where r is the radius.