Question

X
The equation of a circle
concentric with the circle
x² + y2 + 2gx + 2 fy+c=0 will
be in the form of​

Answer 1

Given equations:

x

2

+y

2

+2gx+2fy+c=0→(I)

∴ Centre → (−g,−f)

and radius =

g

2

+f

2

−c

and x

2

+y

2

+2gx+2fy+k=0→(II)

Again, centre → (−g,−f)

and radius =

g

2

+f

2

−k

Same centre and different radii,

hence concentric circles.

∴ Given statement is true.

(ifk=c).