Determine the center and radius of the following circle equation: x2 + y2 + 10x + 20y + 109 = 0
Center:
Radius:
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problem 1 out of max

The equation of the circle  (x + 5 )² + ( y + 10 )² = (4)²

Center of the circle ( h, k) = ( -5 , -10)

Radius of the circle     ' r' = 4

Step-by-step explanation:

Explanation:-

Given circle equation is x² + y² +10 x + 20 y +109 =0

                                     x² +10 x +  y² + 20 y +109 =0

  x² +2 (5) (x)+(5)² -(5)²+ y² +2(10) y + (10)²-(10)² +109 =0

By using formula

(a+b)² = a² + 2 a b + b²

(x + 5 )² + ( y + 10 )² - 25 - 100 + 109 = 0

(x + 5 )² + ( y + 10 )² - 16 = 0

(x + 5 )² + ( y + 10 )² = 16

(x + 5 )² + ( y + 10 )² = (4)²

The standard equation of the circle  ( x - h )² + ( y -k)² = r²

Center of the circle ( h, k) = ( -5 , -10)

Radius of the circle     ' r' = 4

Conclusion:-

The equation of the circle  (x + 5 )² + ( y + 10 )² = (4)²

Center of the circle ( h, k) = ( -5 , -10)

Radius of the circle     ' r' = 4

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet