Equations of Circles in Standard Form

Front

What is the center of the circle with the equation (x+2)²+(y-4)²=41?

Back

(-2, 4)

Front

What is the standard equation of a circle?

Back

(x-h)² + (y-k)² = r²

Front

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

Back

(x + 5)² + (y - 2)² = 36

Front

What is the equation of the circle with center (-1, -1) and radius 3?

Back

(x + 1)² + (y + 1)² = 9

Front

What is the radius of the circle (x+7)²+(y-2)²=144?

Back

12

Front

What does the variable 'r' represent in the standard equation of a circle?

Back

The radius of the circle.

Front

If the center of a circle is at (h, k), what does 'h' and 'k' represent?

Back

The x-coordinate and y-coordinate of the center of the circle, respectively.

Front

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

Back

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

Front

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

Back

The radius is the square root of the constant on the right side of the equation (r = √r²).

Front

What is the equation of a circle with center (0, 0) and radius 5?

Back

x² + y² = 25