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

Solution:

Given circle equation x² + y² + 8x - 6y + 21=0

We have standard equation of circle,

x² + y² - 2ax - 2by + (a² + b² - m²) = 0 with centre(a, b) and radius “m”

To find radius, we extract the “m” term

m = √(a² +b² ) --- (a)

Compare the terms (a² + b² - m²) = 21

 -2ax = 8x ⇒ a = -4

 -2by = -6 ⇒ b = 3

 Put a,b values in eq(a)

 Radius = m = √(a² +b² ) =√((-4)² +3²)

= √(16 +9)

= √25 = 5

 Radius = 5 units

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

Summary:

The radius of a circle whose equation is x² + y² + 8x - 6y + 21 = 0 is 5units.