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What is the radius of a circle whose equation is x² + y² + 8x − 6y + 21 = 0 ? O 2 units O 3 units O 4 units O 5 units

1 Answer

5 votes

Answer:

radius = 2 units

Explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

(h, k ) are the coordinates of the centre and r is the radius

given

x² + y² + 8x - 6y + 21 = 0 ( subtract 21 from both sides )

x² + y² + 8x - 6y = - 21 ( collect x/ y terms together )

x² + 8x + y² - 6y = - 21

using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(4)x + 16 + y² + 2(- 3)y + 9 = - 21 + 16 + 9

(x + 4)² + (y - 3)² = 4 ← in standard form

with r² = 4 , then

r =
√(4) = 2 units

User Lajos Molnar
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