Question : $x$ varies inversely as the square of $y$. Given that $y=2$ for $x=1$, the value of $x$ for $y=6$ will be equal to:
Option 1: 3
Option 2: 9
Option 3: $\frac{1}{3}$
Option 4: $\frac{1}{9}$
Correct Answer: $\frac{1}{9}$
Solution :
$x$ varies inversely as a square of $y$.
$⇒x=\frac{a}{y^2}$, where $a$ is constant
At $y=2, x=1$
$⇒1=\frac{a}{2^2}$
$⇒a=4$
If $y=6$, then,
$\therefore x=\frac{4}{6^2}=\frac{4}{36}=\frac{1}{9}$
Hence, the correct answer is $\frac{1}{9}$.
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