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Lunna [17]
3 years ago
8

What's the center of a circle whose equation is (x – 14)2 + (y + 21)2 = 64?

Mathematics
1 answer:
kvasek [131]3 years ago
7 0

Answer:

The center of the circle is:

  • \left(a,\:b\right)=\left(14,\:-21\right)

Thus, option (2) is true.

Step-by-step explanation:

The circle equation is given by

\left(x-a\right)^2+\left(y-b\right)^2=r^2

here,

  • r =  raduis
  • center = (a, b)

Given the equation

\left(x-14\right)^2+\left(y+21\right)^2=64

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

\left(x-14\right)^2+\left(y-\left(-21\right)\right)^2=8^2

comparing with the circle equation

\left(x-a\right)^2+\left(y-b\right)^2=r^2

Therefore, the center of the circle is:

  • \left(a,\:b\right)=\left(14,\:-21\right)

Thus, option (2) is true.

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