Respuesta :

absor201

Answer:

The center of the circle is:

  • [tex]\left(a,\:b\right)=\left(14,\:-21\right)[/tex]

Thus, option (2) is true.

Step-by-step explanation:

The circle equation is given by

[tex]\left(x-a\right)^2+\left(y-b\right)^2=r^2[/tex]

here,

  • r =  raduis
  • center = (a, b)

Given the equation

[tex]\left(x-14\right)^2+\left(y+21\right)^2=64[/tex]

[tex]\mathrm{Rewrite}\:\left(x-14\right)^2+\left(y+21\right)^2=64\:\mathrm{in\:the\:form\:of\:the\:standard\:circle\:equation}[/tex]

[tex]\left(x-14\right)^2+\left(y-\left(-21\right)\right)^2=8^2[/tex]

comparing with the circle equation

[tex]\left(x-a\right)^2+\left(y-b\right)^2=r^2[/tex]

Therefore, the center of the circle is:

  • [tex]\left(a,\:b\right)=\left(14,\:-21\right)[/tex]

Thus, option (2) is true.

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