Radius Distance of A Circle

Front

What is the definition of the radius of a circle?

Back

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

Front

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

Back

To determine the position of a point relative to a circle, compare the distance from the point to the center of the circle with the radius. If the distance is less than the radius, the point is inside; if equal, it is on; if greater, it is outside.

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

Given the equation (x - 1)² + (y + 2)² = 16, what is the radius?

Back

The radius is 4.

Front

What is the center of the circle represented by the equation (x + 3)² + (y - 1)² = 36?

Back

The center is (-3, 1).

Front

Calculate the distance between the center (2, 3) and the point (5, 7).

Back

The distance is 5.

Front

If a circle has a radius of 10, what is the area of the circle?

Back

The area is 314.16 square units (using the formula A = πr²).

Front

What is the circumference of a circle with a radius of 5?

Back

The circumference is 31.42 units (using the formula C = 2πr).

Front

How do you find the radius from the equation of a circle?

Back

To find the radius from the equation (x - h)² + (y - k)² = r², take the square root of the value on the right side of the equation.

Front

What does it mean if a point lies on the circle?

Back

If a point lies on the circle, the distance from the point to the center is exactly equal to the radius.