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**Hint:**It is given as \[\text{A}\] is directly proportional to \[\text{B}\]. Then we can write this as \[\text{A }\!\!\alpha\!\!\text{ B}\] and we can equate it by introducing a constant between \[\text{A}\] and \[\text{B}\] as \[\text{A = KB}\] where \[\text{K}\] is constant.

For finding the value of \[\text{K}\] you need the values of \[\text{A}\] and \[\text{B}\] and then you can put it in equation to get the value of \[\text{K}\].

**Complete step by step solution:**It is given in the question that \[\text{Y}\] is inversely proportional to the square of \[\text{X}\] we can write it as \[\text{Y }\alpha \text{ }\dfrac{1}{{{x}^{2}}}\] and we can introduce constant \[\text{C}\]

\[\therefore \text{Y = }\dfrac{\text{C}}{{{x}^{2}}}\,......\,(1)\]

We have to find a equation connecting \[\text{Y}\] and \[\text{X}\] when \[\text{Y = 50}\] and \[\text{X = 2}\]

So, the proportional equation becomes

\[50\,=\,\dfrac{\text{C}}{{{\left( 2 \right)}^{2}}}\]

\[\text{C}\,\text{=}\,\text{50}\times {{2}^{2}}\]

\[\text{50}\times 4\]

\[\text{C}\,=\,200\]

Putting the value of \[\text{C}\] in equation \[(1)\] we get,

\[\text{Y}\,=\,\dfrac{200}{{{\text{X}}^{2}}}\], which could be written as \[{{x}^{2}}y\,\,=\,200\]

This is an equation connecting \[\text{Y}\] and \[\text{X}\] when \[\text{Y = 50}\] and \[\text{X = 2}\]

**Additional Information:**

When \[y\] is inversely proportional to the square of \[x\]. It means if \[x\] is increased two times then, the value of \[y\] decreases four times.

For example:

If \[x\,=\,2\]

\[y\,=\,\dfrac{\text{C}}{{{x}^{2}}}\,=\,y\,=\,\dfrac{\text{C}}{{{2}^{2}}}\,=\,\dfrac{\text{C}}{4}\]

The graph that represents this equation clearly.

Let us discuss the case where \[x\] is positive, if \[x\] is positive, then

As \[x\to \infty ,\,y\to 0\] and vice versa.

i.e if \[x\] gets larger, \[y\] gets smaller and vice versa.

Sometimes the question comes \[y\] is inversely proportional to \[x\] it can simply be written as \[y\,=\,\dfrac{\text{C}}{x}\,\]

**Note:**

When putting values of \[y\] and \[x\] in the given equation carefully solve and find the value of the constant you assumed.

It is not necessary to assume constant as \[\text{C}\] you can assume any variable you wish.

The sign \[\alpha \] is used for both inversely proportional and directly proportional questions.

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