# What is the radius of a circle whose equation is x² + y² + 8x – 6y + 21 = 0?

Answer: The radius of the circle is approximately 4.47 units. This is calculated by completing the square to rewrite the equation in the standard form and then finding the radius.

## Circle Geometry and Algebra

To find the radius of a circle from the equation x² + y² + 8x – 6y + 21 = 0, we first complete the square for both x and y terms to bring the equation to the standard circle form (x-h)² + (y-k)² = r². From this, we can determine the radius. This process blends algebra and geometry, teaching valuable skills in manipulating equations and understanding shapes.

## FAQ on Circle Geometry and Algebra

### What is the radius of a circle with the equation x² + y² – 10x + 14y – 23 = 0?

The radius is approximately 7.07 units.

### How do you find the radius of a circle with the equation x² + y² + 6x – 2y + 6 = 0?

The radius is approximately 2.24 units.

### What is the radius of a circle whose equation is x² + y² – 4x + 8y – 5 = 0?

The radius is approximately 3.61 units.

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