Answer:√30
Step-by-step explanation:
2g=4
g=4/2
g=2
2f=8
f=8/2
f=4
c=-10
Radius=√(g^2+f^2-c)
Radius=√(2^2+4^2-(-10))
Radius=√(4+16+10)
Radius=√(30)
[tex]\sqrt{30}[/tex] is the radius of the circle with equation [tex]x^{2} +y^{2} +4x+8y-10[/tex][tex]=0[/tex]
What is radius of the circle?
In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin radius, meaning ray but also the spoke of a chariot wheel.
According to question, we have the following equations:
[tex]x^{2} +y^{2} +4x+8y-10[/tex][tex]=0[/tex]
From the equation of circle, we have
[tex]2g=4\\g=4/2\\g=2\\2f=8\\f=\frac{8}{2} \\ \\f=4\\c=-10[/tex]
Radius of the circle [tex]=\sqrt{(g^2+f^2-c)}[/tex]
[tex]=\sqrt{4+16+10)}[/tex]
[tex]=\sqrt{30}[/tex]
Hence, we can conclude that [tex]\sqrt{30}[/tex] is the radius of the circle with equation
[tex]x^{2} +y^{2} +4x+8y-10[/tex][tex]=0[/tex]
Learn more about radius of the circle here:
https://brainly.com/question/27151718?referrer=searchResults
#SPJ2
