The equation of a circle is given by \({x}^{2}+{y}^{2}={a}^{2}\), where a is the radius. If the equation is modified to …

The equation of a circle is given by \({x}^{2}+{y}^{2}={a}^{2}\), where a is the radius. If the equation is modified to change the origin other than (0,0), then find out the correct dimensions of \(A\) and \(B\) in a new equation: \((x-At{)}^{2}+{\left(y-\frac{t}{B}\right)}^{2}={a}^{2}\). The dimensions of t is given as \(\left[{T}^{-1}\right]\).

[JEE Main 2023, 29 Jan (Shift 2)]