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 from the equation (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 + 4)² = 121?

Back

The center of the circle is (3, -4).

Front

If the radius of a circle is 5, what is the equation of the circle centered at (0, 0)?

Back

The equation is x² + y² = 25.

Front

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

Back

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

Front

How do you convert the diameter of a circle to its radius?

Back

To convert the diameter to radius, divide the diameter by 2.

Front

What is the radius of a circle with the equation (x + 2)² + (y - 3)² = 4?

Back

The radius is 2.

Front

What is the equation of a circle with center (4, 2) and radius 5?

Back

The equation is (x - 4)² + (y - 2)² = 25.

Front

What is the significance of the number on the right side of the equation of a circle?

Back

The number on the right side of the equation (r²) represents the square of the radius.

Front

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

Back

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