Amazing Circle!
Geometry
Level
pending
The equation of a circle is, (X)^2 + (Y)^2 + 80X + 80Y + 3201 = 0 Then, which one is the center of this circle?
None of these
(40 , 40)
No such Real Circle Exists
(-40 , -40)
(80 , 80)
(-80 , -80)
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1 solution
The general equation of a circle is = (X)^2+(Y)^2+2gX+2fY+c = 0. The center is (-g , -f) & The radius is (sqrt(g^2+f^2-c)). Then, comparing the given equation with the general one, We easily get (g)=(-40), (f)=(-40) & (c)= 3201; So, The RADIUS is (sqrt(3200-3201)) = sqrt(-1) = i which is an imaginary number. Therefore, No such REAL Circle exists.