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Nirina7

the main formula of a circle is (x-a)²+(y-b)²= r², where (a,b) is the center of the circle
x2+y2+8x−14y+56= x2+8x+y2−14y+56=(x+4)²-16+(y-7)²- 49+ 56=0
it means (x+4)²+(y-7)²- 9=0 and it implies  (x+4)²+(y-7)²=9
so r²=9, and finally  r =3

Answer:  The radius of the circle is 3 units.

Step-by-step explanation:  The given equation of the circle is

\(x^2+y^2+8x-14y+56=0~~~~~~~~~~~~~~~(i)\)

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

\((x-g)^2+(y-h)^2=r^2.\)

From equation (i), we have

\(x^2+y^2+8x-14y+56=0\\\\\Rightarrow (x^2+8y+16)+(y^2-14y+49)-16-49+56=0\\\\\Rightarrow (x+4)^2+(y-7)^2=9\\\\\Rightarrow (x+4)^2+(y-7)^2=3^2.\)

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.

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