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

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 in the equation (x + 3)² + (y - 2)² = 16?

Back

The center of the circle is (-3, 2).

Front

If the equation of a circle is (x - 1)² + (y + 4)² = 25, what is the radius?

Back

The radius is 5, since √25 = 5.

Front

Write the equation of a circle with center (2, -3) and radius 4.

Back

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

Front

What does the term (x - h) represent in the circle equation?

Back

The term (x - h) represents the horizontal distance from the center of the circle to a point on the circle.

Front

What does the term (y - k) represent in the circle equation?

Back

The term (y - k) represents the vertical distance from the center of the circle to a point on the circle.

Front

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

Back

Substitute the point (x, y) 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 radius of the circle given by the equation (x - 5)² + (y + 1)² = 36?

Back

The radius is 6, since √36 = 6.

Front

What is the center of the circle in the equation (x - 4)² + (y + 3)² = 9?

Back

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