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: $(x-A t)^2+\left(y-\frac{t}{B}\right)^2=a^2$.The dimensions of $t$ is given as $\left[ T ^{-1}\right]$.
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: $(x-A t)^2+\left(y-\frac{t}{B}\right)^2=a^2$.The dimensions of $t$ is given as $\left[ T ^{-1}\right]$.
- [JEE MAIN 2023]
- A
$A =\left[ L ^{-1} T \right], B =\left[ LT ^{-1}\right]$
- B
$A =[ LT ], B =\left[ L ^{-1} T ^{-1}\right]$
- C
$A =\left[ L ^{-1} T ^{-1}\right], B =\left[ LT ^{-1}\right]$
- D
$A =\left[ L ^{-1} T ^{-1}\right], B =[ LT ]$
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