Respuesta :

check the picture below.

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-6}{ h},\stackrel{4}{ k})\qquad \qquad radius=\stackrel{6}{ r} \\\\\\\ [x-(-6)]^2+[y-4]^2=6^2\implies (x+6)^2+(y-4)^2=36[/tex]
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Lanuel

The equation of the circle shown in the graph is equal to [tex](x + 6)^2 + (y - 4)^2 = 36[/tex]

Form the graph, we can deduce the following points:

The center of the circle is denoted by the black dot and we can see that the values are -6 and 4 respectively.

  • Center (h, k) = (-6, 4)

Also, the diameter of the circle is:

Diameter = 12 units

Radius = [tex]\frac{Diameter}{2} = \frac{12}{2} = 6 \;units[/tex]

Mathematically, the standard form of the equation of a circle is given by;

  .....equation 1

Where;

  • h and k represents the coordinates at the center.
  • r represents the radius of the circle.

Substituting the values into eqn 1, we have:

[tex](x - [-6])^2 + (y - 4)^2 = 6^2\\\\(x + 6)^2 + (y - 4)^2 = 36[/tex]

Read more: https://brainly.com/question/23691177

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