Question

Which two statements are true? Choices and equation are attached.

Answer 1

As

• The center of the circle is (-6, 11)

• The radius of the circle is 6

Therefore, the statements A and C are true.

Explanation:

Given the equation of the circle

`\left(x+6\right)^2+\left(y-11\right)^2=36`

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

`\mathrm{is\:the\:circle\:equation\:with\:a\:radius\:r,\:centered\:at}\:\left(a,\:b\right)`

`\mathrm{Rewrite}\:\left(x+6\right)^2+\left(y-11\right)^2=36\:\mathrm{in\:the\:form\:of\:the\:standard\:circle\:equation}`

`\left(x-\left(-6\right)\right)^2+\left(y-11\right)^2=6^2`

`\mathrm{Therefore\:the\:circle\:properties\:are:}`

`\left(a,\:b\right)=\left(-6,\:11\right),\:r=6`

Thus,

• The center of the circle is (-6, 11)

• The radius of the circle is 6

Therefore, the statements A and C are true.