Write the equations of 2 circles that are concentric

Two circles or more than that are said to be concentric if they have the same centre but different radii. 

Let, x22 + y22 + 2gx + 2fy + c = 0 be a given circle having centre at (- g, - f) and radius = g2+f2−c−−−−−−−−−√g2+f2−c.

Therefore, the equation of a circle concentric with the given circle x22 + y22 + 2gx + 2fy + c = 0 is

x22 + y22 + 2gx + 2fy + c' = 0 

Both the circle have the same centre (- g, - f) but their radii are not equal (since, c ≠ c')

Similarly, the equation of a circle with centre at (h, k) and radius equal to r, is (x - h)22 + (y - k)22 = r22.

Therefore, the equation of a circle concentric with the circle (x - h)22 + (y - k)22 = r22 is  (x - h)22 + (y - k)22 = r1122, (r11 ≠ r)      

Assigning different values to r11 we shall have a family of circles each of which is concentric with the circle (x - h)22 + (y - k)22 = r22.

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