Answer:
The radius = 4
Step-by-step explanation:
considering the equation
[tex]\left(x+2\right)^2+\left(y-4\right)^2=16[/tex]
As the standard form of the circle is
[tex]\left(x-h\right)^2+\left(y-k\right)^2=r^2[/tex]
Match the values in this circle to those of the standard form.
- The variable [tex]r[/tex] represents the radius of the circle,
- [tex]h[/tex] represents the x-offset from the origin, and
- [tex]k[/tex] represents the y-offset from origin.
[tex]\mathrm{Rewrite}\:\left(x+2\right)^2+\left(y-4\right)^2=16\:\mathrm{in\:the\:form\:of\:the\:standard\:circle\:equation}[/tex]
[tex]\left(x-\left(-2\right)\right)^2+\left(y-4\right)^2=4^2[/tex]
[tex]\mathrm{Therefore\:the\:circle\:properties\:are:}[/tex]
[tex]\left(h,\:k\right)=\left(-2,\:4\right),\:r=4[/tex]
Therefore, the radius = 4
