The equation of a circle is #x^2+y^2+8x−14y+56=0# . What is the radius of the circle?

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Answer 1 · 2018-01-04T06:15:29

r = 3

Equation General:

#(x - h)^2 + (y - k)^2 = r^2#

Re-arranging:

#(x^2 + 8x) + (y^2 - 14y) + 56= 0#

Making squares by analogy (method)
1): divide each no square variable coefficient
#8/2 = 4#
#14/2 = 7#

2): make square each divided coefficient
#4^2 => 16#
#7^2 => 49#

3) Substitute previous coefficients in general equation:
#(x^2 + 8x + 16) + (y^2 - 14y + 49) + (56 - 16 - 49)= 0#

#(x + 4)^2 + (y - 7)^2 = (9)^2#

#r^2 = 9#

#r = 3#