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Q. The equation $x^2+y^2=r^2$ represents a family of concentric circles centered at the ...$A$... and having ...$B$ ... radii.
Here, $A$ and $B$ are respectively

Differential Equations

Solution:

Let us consider the equation
$x^2+y^2=r^2 .....$(i)
By giving different values of $r$, we get different members of the family e.g., $x^2+y^2=1, x^2+y^2=4, x^2+y^2=9$, etc.
image
Thus, Eq. (i) represents a family of concentric circles centred at the origin and having different radii.