What is the radius of a circle whose equation is x2 + y2 + 8x – 6y + 21 = 0? units
2 answers:
Answer:
radius = 2
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r the radius
Given
x² + y² + 8x - 6y + 21 = 0
Use the method of completing the square to obtain standard form
Collect the x- terms and y- terms together and subtract 21 from both sides
x² + 8x + y² - 6y = - 21
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 centre (- 4, 3) and radius = = 2
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