What is the center and radius of the circle with the given equation?
1 answer:
Answer:
(- 1, - 4 ) and r = 5
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 is the radius
To obtain this form from the given equation use the method of completing the square.
Given
x² + y² + 2x + 8y = 8 ( rearrange by collecting x and y terms )
x² + 2x + y² + 8y = 8
To complete the square
add ( half the coefficients of the x/ y terms )² to both sides
x² + 2(1)x + 1 + y² + 2(4)x + 16 = 8 + 1 + 16
(x + 1)² + (y + 4)² = 25 ← in standard form
with centre (h, k ) = (- 1, - 4 ) and r = = 5
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