Answer:
1st and 2nd options
Explanation:
Using the method of completing the square to obtain standard form
(13)
Rearrange the given equation so x and y terms are together, that is
x² + 24x + y² + 30y + 353 = 0 ( subtract 353 from both sides )
x² + 24x + y² + 30y = - 353
To complete the square
add ( half the coefficients of the x/ y term)² to both sides
x² + 2(12)x + 144 + y² + 2(15)y + 225 = - 353 + 144 + 225
(x + 12)² + (y + 15)² = 16
(x + 12)² + (y + 15)² = 4² ← in standard form
with centre = (- 12, - 15 ) and radius = 4
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(14)
As in number 13
x² - 22x + y² + 16y = - 181
Complete the square
x² + 2(-11)x + 121 + y² + 2(8)y + 64 = - 181 + 121 + 64
(x - 11)² + (y + 8)² = 4
(x - 11)² + (y + 8)² = 2² ← in standard form
with centre = (11, - 8 ) and radius = 2