Answer:
The answer to your question is below
Step-by-step explanation:
The standard form of the equation
(x - h)² + (y - k)² = r²
13.- x² + y² - 26y + 165 = 0
-Group like terms
(x² ) + (y² - 26y ) = -165
-Complete perfect square trinomials
(x² ) + (y² - 26y + 13²) = -165 + 13²
-Simplify
(x² + 0)² + (y - 13)² = -165 + 169
-Result
x² + (y - 13)² = 4
14.
x² + y² + 2x + 24y + 140 = 0
-Group like terms
(x² + 2x ) + (y² + 24y ) = -140
-Complete perfect square trinomials
(x² + 2x + 1²) + (y² + 24y + 12²) = -140 + 1 + 144
-Simplify
(x + 1)² + (y + 12)² = 5
15.-
A ( -1, -16)
B (-1, -10)
-Calculate the midpoint
Xm = (-1 -1) /2 = -1
Ym = (-16 - 10)/2 = -13
Center = (-1, -13)
-Calculate the radius
dAB = [tex]\sqrt{(-10 + 16)^{2} + (-1 + 1)^{2}}[/tex]
-Simplify
dAB = [tex]\sqrt{6^{2}+ 0^{2}}[/tex]
dAB = [tex]\sqrt{36}[/tex]
-Result
dAB = 6
radius = 6/2 = 3
-Equation
(x + 1)² + (y + 13)² = 3²
(x + 1)² + (y + 13)² = 9
