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

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

Back

The center of a circle is the point (h, k) in the equation (x-h)² + (y-k)² = r², which is equidistant from all points on the circle.

Front

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

Back

The radius can be found by taking the square root of the number on the right side of the equation in standard form: (x-h)² + (y-k)² = r².

Front

What is the center of the circle with equation x² + y² = 25?

Back

The center is (0, 0).

Front

In the equation (x-1)² + (y+2)² = 36, what is the radius?

Back

The radius is 6.

Front

What is the equation of a circle with center (4, -3) and radius 5?

Back

The equation is (x-4)² + (y+3)² = 25.

Front

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

Back

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

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, the point is inside; if equal, on the circle; if greater, outside.

Front

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

Back

It represents the square of the radius (r²) in the equation (x-h)² + (y-k)² = r².

Front

What is the center of the circle defined by the equation (x+5)² + (y-1)² = 16?

Back

The center is (-5, 1).