The equation of a circle is given by x ^ 2 + y ^ 2 = a ^ 2 , where...

Principle of Homogeneity states that dimensions of each of the terms of a dimensional equation on both sides should be the same. Then,

${\left(x - At\right)}^{2} + {\left(y - \dfrac{t}{B}\right)}^{2} = {a}^{2}$

For first term,

\left[At\right] = \left[x\right] ⇒ A \times \dfrac{1}{T} = L$</p><p>$∴ \left[A\right] = {T}^{1}{L}^{1}$</p><p>For the second term,</p><p>\left[\dfrac{t}{B}\right] = \left[y\right]$

$⇒ \dfrac{1}{T\left[B\right]} = L$

$⇒ \left[B\right] = {T}^{- 1}{L}^{- 1}$