Answer: The radius of the circle is 3 units.
Step-by-step explanation: The given equation of the circle is
![x^2+y^2+8x-14y+56=0~~~~~~~~~~~~~~~(i)](https://tex.z-dn.net/?f=x%5E2%2By%5E2%2B8x-14y%2B56%3D0~~~~~~~~~~~~~~~%28i%29)
We are to find the radius of the circle (i).
The standard equation of a circle with centre (g, h) and radius 'r' units is given by
![(x-g)^2+(y-h)^2=r^2.](https://tex.z-dn.net/?f=%28x-g%29%5E2%2B%28y-h%29%5E2%3Dr%5E2.)
From equation (i), we have
![x^2+y^2+8x-14y+56=0\\\\\Rightarrow (x^2+8y+16)+(y^2-14y+49)-16-49+56=0\\\\\Rightarrow (x+4)^2+(y-7)^2=9\\\\\Rightarrow (x+4)^2+(y-7)^2=3^2.](https://tex.z-dn.net/?f=x%5E2%2By%5E2%2B8x-14y%2B56%3D0%5C%5C%5C%5C%5CRightarrow%20%28x%5E2%2B8y%2B16%29%2B%28y%5E2-14y%2B49%29-16-49%2B56%3D0%5C%5C%5C%5C%5CRightarrow%20%28x%2B4%29%5E2%2B%28y-7%29%5E2%3D9%5C%5C%5C%5C%5CRightarrow%20%28x%2B4%29%5E2%2B%28y-7%29%5E2%3D3%5E2.)
Comparing the above equation with the standard equation of a circle, we get
r = 3.
Thus, the radius of the given circle is 3 units.