primesonic11
Answered

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5. A circle has the equation x2 + 8x + y2 - 16y - 64 = 0.
Rewrite the equation in standard form and identify its
center coordinates and radius length.
Answer (Show your work):

Sagot :

Answer:

Step-by-step explanation:

Y2-12y=-29= the answer is 6

Answer:

centre = (- 4, 8 ) , radius = 12

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 abd r is the radius

given

x² + 8x + y² - 16y - 64 = 0 ( add 64 to both sides )

x² + 8x + y² - 16y = 64

using the method of completing the square

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

x² + 2(4)x + 16 + y² + 2(- 8)y + 64 = 64 + 16 + 64

(x + 4)² + (y - 8)² = 144 ← in standard form

with centre (- 4, 8 ) and r = [tex]\sqrt{144}[/tex] = 12

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