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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